Oh, I can kind of answer this one, albeit in a very focused manner! I recently finished writing a book about the history of nuclear power in Japan and the first chapter is all about the pre-atomic industrialisation of Japan, with a focus on the power industry.

The very short answer is that Japan found itself in the extremely rare and fortuitous position of being able to pick and choose from the best elements of society, science and industry that the world's industrialised countries had developed. It made no sense to ignore all of that and try to forge their own way from scratch - they would never catch up.

The longer answer (and I will try to keep this short because I could go on for hours about it) is that Japan's elites were somewhat divided on the issue. America sailed in and forced the historically isolationist Japan to open its borders and trade with the outside world in the 1850s, which led to some major culture shock. The country had stagnated in pretty much all ways a country can during its isolation, which began in the 1630s. With no apparent end to the setbacks wrought by such profound changes, the Shogunate leaders’ once-irrefutable and unbreakable hold over Japan gradually weakened through a combination of constant and often unrealistic foreign demands; massive economic instability, rising inflation and unemployment from the sudden influx of foreign currency; a succession of mighty earthquakes and tsunami in the Nankaidō and Tōkai regions, killing close to 100,000 people in the mid- to late-1850s; a wave of cholera from outsiders that brought sickness and death on a massive scale; rearmament by the country’s once-cooperative lords seeking to reinforce control over their domains; and many other complex social factors. Intense disaffection manifested among the people in a social movement known as Sonnō Jōi: “Revere the Emperor, Expel the Barbarians.”

Within a few years this all led to the rise of Emperor Meiji and fall of the Shogunate after an 18-month civil war. As you alude to in your question, the fledgling Meiji government’s new policies demonstrated, within a few short years, a complete about-face among what had been ardent opponents of Western technology and style of governance. This apparent betrayal of honour-bound principles – the Jōi element of Sonnō Jōi – was not as unexpected as it may appear, however, as Japan was ripe for modernisation and industrialisation, as most forward-thinkers knew. The nation boasted widespread educational institutions, government promotion of industrial and agricultural growth, established communications and transportation networks, and, excluding perhaps the years since America’s arrival, peace and political stability. Just as Emperor Meiji took office, the most powerful lords sent a letter to the imperial court, arguing that Japan should accept Western influence and avoid “the bad example of the Chinese, who fancy themselves alone to be great and worthy of respect, and despising the foreigners as little better than beasts, have come to suffer defeat at their hands.”

The government abolished its old feudal domain system and combined the regions into 47 prefectures in 1871. Later that year, around 100 government officials, military leaders, prominent scholars, statesmen and students – under the umbrella title of the Iwakura Mission, after the group’s leader, Tomomi Iwakura – travelled around Europe and the United States until 1873 to re-negotiate treaties and learn about the world and the latest technologies. They concluded that economic self-sufficiency through educational reform, industrialisation and military strength was not only achievable but was vital to securing Japan’s long-term future. To help promote this radical new belief, Emperor Meiji’s government adopted the ancient Confucian slogan Fukoku kyōhei (“Rich Country, Strong Army”) as its principal goal and driving force. Military reform introduced a requisite four-year national conscription for all males and the abolition of the legendary samurai warrior class.

Japan found itself in the advantageous position, as I mentioned at the top, of being able to pick and choose the best elements from the world’s industrialised nations and then adapt them for its own use. A new army mimicked the Prussian army, for example, while the police force copied the French approach. The penal code was first based on imperial China’s version of the Confucian legal principles but was changed in 1907 to a German model. The postal service, too, underwent reform, modelled on the government-operated British example of a nationwide flat fee for deliveries. By the late 1870s, the Meiji government had erected a spider’s web of telegraph lines between all major cities, nationalised the country’s most valuable natural resources (including its 11 largest coal mines) and built a fleet of cutting-edge factories and shipyards using public funds and the latest technologies imported from Europe. Such initiatives worked to an extent, with coal production soaring from 600,000 tons of coal in 1875 to 13 million by 1905, but the enormous expenditure and typical bureaucratic inefficiencies of government rendered them unprofitable. Most sites were handed back to the private sector for a pittance a few decades later to reduce the national deficit and inflation. From here the government had little direct involvement in industry for a number of years (though they did retain complete control over the telegraph industry), but their efforts had not been in vain: the economy began to thrive.

Private companies such as The Tokyo Electric Light Company (known today as TEPCO - the company which operated the ill-fated Fukushima Daiichi nuclear power station) were pioneers in importing foreign power technologies and the government basically left them to it, not imposing any real regulations at all until May 1896. Even then, the government kept their hands off for the most part, so Meiji himself really had very little involvement in some respects past the initial stages.

/u/R_Spc's answer isn't bad, but I think I would like to add:

(1) the Meiji Emperor himself wasn't actually that powerful a figure. Certainly he had more power than past emperors, but he was not a true, all-powerful despot through the Restoration.

(2) It depends on what you mean by "modernizing" and "Western." Many observers and some today characterize the shift from the "feudal" (let's put aside whether or not it was) system of the Tokugawa shogunate to the centralized imperial state as "Westernizing," but to the contemporary Japanese, it was characterized as a return to ancient tradition. Historian Mark Ravina (who I will also cite below) calls this "radical nostalgia," wherein Meiji reforms and practices that we think of as "modernizing" were justified as part of a program of returning to a mythical, ancient past.

(3) But to address why Japan "westernized," the simple answer is because they didn't see it that way. They adopted Western ideas without construing them as necessarily Western, a process that Ravina calls "cosmopolitan chauvinism." In effect, Japanese leaders and thinkers integrated Western cultural products and values into their own society by asserting that they were actually reflective of universal, rather than culturally relative, principles. In the same way, a more ancient Japanese society had integrated Confucian principles without necessarily "Sinicizing" or becoming "more Chinese," at least not from the perspective of those in Meiji Japan. From this perspective, Meiji Japan was not adopting "Western" cultural values; it was recognizing self-evident, universal principles and adopting them in the way it had done with Confucianism, Buddhism, etc.

(4) Not everyone always agreed on how much to adapt from the West! As u/R_Spc points out, the Iwakura Mission was instrumental to bringing back information from the West. But... while the Iwakura Mission toured the West, the rusu seifu (caretaker government) ruled back at home, and they had a very different vision of how Japan would "modernize," and thought it could happen a lot easier and faster than those who went on the Iwakura Mission, especially as they idealized the revolutionary fervor of countries like France, aspiring to change quickly and dramatically. So while the Iwakura Mission was abroad, the caretaker government engaged in enormous reforms (or at least attempted; they had a hard time implementing these sweeping proclamations), and the reforms that constituted "Westernization" often were adapted from France, rather than the ascendant Germany. One example of this was the government's Eto Shinpei and his desire for "rapid adoption" of the Napoleonic Code in Japan. Moreover, they thought Japan should take the bold step of adapting to the West by more aggressively engaging in imperialism, being strong advocates of an invasion of Korea and China. The Iwakura Mission, by contrast, was generally of the mind that "progress" should be more measured and incremental, and they were astonished by the ascendance of German power in the wake of the 1870 Franco-Prussian War. They thought Japan, meanwhile, had a much longer way to go. Both sides wanted to have Japan adapt in accordance with the West, but they disagreed in what ways they should and even what models to emulate, largely because the Iwakura Mission had seen a perceived failure of "revolutionary passion" in France vs German "realpolitik."

Given this conflict, when the caretaker government and the returning Iwakura Mission attempted to reunite, it caused a political crisis in 1873. Eventually, the side of the Iwakura Mission would win out, but those members of the caretaker government that lost power took to adopting some "Western" principles of democracy and popular protest in opposition to the new balance of power, even invoking Confucian principles with concepts such as "no taxation without representation."

Still, while they had trouble implementing reforms, the caretaker government did do stuff while the Iwakura Mission was away, touring the West. And their politics left a legacy of military populism that obviously had ramifications later, when Japan did start to engage in the exact imperialist actions they had advocated decades earlier. So even in "Westernizing," there wasn't necessarily a unified vision of how to develop Japan during the Meiji era.

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Ravina, Mark. To Stand With the Nations of the World: Japan's Meiji Restoration in World History. Oxford University Press US, 2020.