Your question is great, but you might not realise just how many different questions are packed into that single line!

First and foremost it is important to define what you mean by “same format”. Do you mean the use of clocks in general? Or do you mean that we conventionally divide the day into 24 hours? Or do you mean the use of time zones based on the same Universal Time? Those are three very different though certainly interrelated questions. Furthermore, the “same format” can even refer to more essential elements: the basic use of timekeeping devices or the abstract act of dividing the day into smaller temporal units. With this in mind, my answer is going to be limited to the emergence of Universal Time and the uniform time system.

The International Meridian Conference in Washington D.C. in 1884 is usually taken as the starting point for creating a uniform system of time and space (Barrows, 2010). At this conference, the meridian passing through the Royal Observatory at Greenwich was recommended as the International Prime Meridian (or Longitude Zero) by many nations (Howse, 1980). In addition, the conference also recommended the adoption of a Universal Day in 24 hour notations (Higgitt and Dolan, 2010). However, these were only recommendations, not laws by which participating nations had to abide by. For instance, France did not support the recommendations and famously continued using its own Paris Meridian until the advent of wireless radio signals. Even when they finally conformed to the recommended system in 1911, they continued legally referring to their time as "Paris Mean Time, minus 9 minutes and 21 seconds" (Kershaw, 2014). What the French case shows is that although there was a more or less international backing to recommending a uniform system of time and space, the decision to adopt it was always made at a national level. As a result, it took until around the 1950s for the majority of nations to conform to this system. Since the decisions were made at national levels, it is impossible to highlight the story of every nation, but I recommend you Vanessa Ogle’s book titled The Global Transformation of Time 1870-1950, which does exactly that. One of my favourite stories from it is the time unification efforts in Southern Africa. For example, the German government requested German Southwest Africa to adopt Central European Time. While the local administration formally accepted this, they continued using a different time (used throughout the region) in practice. Cue constant bickering about this for decades.

As you can guess from these examples (and as answers on AskAnthropologists also pointed it out), there was very much a political dimension to these debates. Whose uniformity was being adopted? How will that impact redrawing the temporal boundaries and time zones of nations? Who will benefit from it and who will lose out? These were actual questions that were being debated at the Conference in 1884, and one of the reasons why France decided not to join in the Conference’s recommendations. The argument that it was a measure of convenience rests on the dominance of British navigational tools (helping travellers determine local time and space with reference to Greenwich) being used by the majority of people involved in navigation. In light of this, the recommendation can be seen either as a legal solidification of the trend towards global “uniformity”, or as a strategic move to solidify the "momentary" British dominance in the long term despite the emergence of other methods (Withers, 2017). The satellite based determination of geographical location became exactly that challenge to the Greenwich system, which is currently contributing to the gradual fall of the Greenwich Prime Meridian into irrelevance (Kershaw, 2019).

Time and its history are big discussion topics among historians, and there are many different questions that can be asked in connection to them. How does our contemporary conception of time (or even the design of Google Calendar) contribute to ordering our everyday lives (Thompson 1967; Wajcman 2019)? How did clock-time mostly used in Western societies gained its image as superior to local time-keeping methods (Frumer, 2018)? What do we actually mean by time and its sameness? Are we perhaps conflating the concepts of regularity, standardisation and cooperation under one single term (Glennie & Thrift, 1996)? Why was it that we decided to draw the line at Greenwich and not through any other point (Withers, 2017)? Were there other similar unification attempts? And if yes, why did we forget about them and why were they not implemented?

So the short answer to your original question: if by “same format” you mean the adoption of uniform time across the globe, then it was a gradual process originating in the 1880s and becoming a dominant way of timekeeping by the middle of the twentieth century. The questions of why it happened this way is a behemoth of a question that your curiosity is bringing you closer and closer to. Just remember that as you are approaching this behemoth, you are there to understand it, not to slay it :)

Sources:

Barrows, A. (2010). The cosmic time of empire: Modern Britain and world literature. Univ of California Press.

Howse, D. (1980). Greenwich Time and the Discovery of the Longitude. Oxford; New York: Oxford University Press.

Higgitt, R., & Dolan, G. (2010). Greenwich, time and ‘the line’. Endeavour, 34(1), 35-39.

Kershaw, M. (2019). Twentieth-century longitude: When Greenwich moved. Journal for the History of Astronomy, 50(2), 221-248.

Ogle, V. (2015). The global transformation of time: 1870–1950. Harvard University Press.

Thompson, E. P. (1967) - Time, work-discipline, and industrial capitalism

Wajcman, J. (2019). How silicon valley sets time. New Media & Society, 21(6), 1272-1289.

Frumer, Y. (2018). Making time: astronomical time measurement in Tokugawa Japan. University of Chicago Press.

Glennie, P., & Thrift, N. (1996). Reworking EP Thompson's Time, work-discipline and industrial capitalism'. Time & Society, 5(3), 275-299.

Withers, C. W. (2017). Zero degrees: Geographies of the prime meridian. Harvard University Press.