The Continental Army didn't have to start from scratch, not entirely. The military system was quite a lot different from today's, and there was a built-in flexibility to take a people's military force from dormant to active by embodying the militia, and by recruiting regulars from the militia. This of course couldn't handle the full load of necessary recruitment, but it did help to ease the burden.

Early battles in the War for Independence were fought almost entirely by colonial militias and British regulars, and early, high-profile come-from-behind victories - or those that could be spun as victories - meant that there was a great deal of enthusiasm for the cause, which, while support had always been fairly high, waxed even more after Bunker Hill and the Siege of Boston. Before I get into mechanisms of recruitment, though, I want to speak to your point about taking on a powerful empire with little hope of success.

Men who looked to join the Continental Army didn't think of it that way. They saw their cause as righteous, it was about freedom from rhetorical slavery, about patriotism against brutal tyranny. The numbers looked bad on paper, but at the start of hostilities the British regulars were massively outnumbered even by the scattered patriot militias, and patriot forces, both militia and regular, typically maintained that numerical superiority throughout the war. It cost time and money and took a good deal of management to shift huge numbers of soldiers from England and other colonies into North America. It took naval superiority to disembark, support, and resupply them. So while one might have looked at numerical assessments of the strength of the empire, its actual ability to project that force was subject to a great deal of complexity. The patriot cause also had a rhetorical and philosophical advantage, which was itself a kind of irony: for all their rhetoric about brutal jackbooted tyranny, many patriots knew that righteous men in England would support them, and from the start, the War for Independence had some political allies even in British parliament. Their cause was rational and righteous, who but Providence might stand against them?

While most of the writing about the conflict from the patriot side comes from officers - whose perspective can be quite a bit different from enlisted men - there were some enlisted men who wrote about the war and their reasons for joining. Joseph Plumb Martin, one of the more well-known voices from the war, writes of his desire to "paint himself a soldier" in a humorous retelling:

And notwithstanding I was told that the British army at that place was reinforced by 15,000 men, it made no alteration in my mind; I did not care if there had been 15 times 15,000, I should have gone just as soon as if there had been but 1,500. I never spent a thought about numbers; the Americans were invincible in my opinion. If anything affected me, it was a stronger desire to see them.

The numbers didn't matter. The cause was holy. Right was on their side. Patriots had already won several engagements, if anyone had believed British regulars invincible at the start of the war, they could be shown they were in error, even by the summer of '76.

All of which is to say that the reason many men joined was not simply because of pay, but because of a kind of patriotic fervor supposedly grounded in rational calculation and adherence to providence. If this sounds like it's an incoherent set of conflicting beliefs, it's because it is. Even Martin, whose reasons for joining were timelessly boyish - the desire for action and adventure, as well as patriotic ardor - describes vividly the appeal of cash bounties paid to enlistees when he first saw a recruiting station in a nearby town:

I found most of the male kind of the people together; soldiers for Boston were in requisition. A dollar deposited upon the drumhead was taken up by someone as soon as placed there and the holder’s name taken, and he enrolled with orders to equip himself as quick as possible. My spirits began to revive at the sight of the money offered; the seeds of courage began to sprout; for, contrary to my knowledge, there was a scattering of them sowed, but they had not as yet germinated; I felt a strong inclination, when I found I had them, to cultivate them. O, thought I, if I were but old enough to put myself forward, I would be the possessor of one dollar, the dangers of war to the contrary notwithstanding.

To Martin, the cash bounty is connected irresistibly to the heroic cause. The sight of the recruitment bounty literally stirred the "seeds of courage" in him, and over the subsequent months he plots and schemes for a way to secure from his grandparents permission to join up. Eventually, he joined a regiment bound for New York on a six-month enlistment, hoping for "a primer" rather than the whole coat of paint. His enlistment is further encouraged by another omnipresent element of military recruitment: homosocial bonding. Martin runs into friends and acquaintances in town, all of them looking to go a-soldiering as well.

But for all his fervor, he hesitates when holding the pen to write his name on the papers. He makes several dry-runs, careful not to touch his pen to the paper, until another friend jostles his shoulder, and the nub scratches a line on the paper. "O, he has enlisted!" the man called. Martin then wrote his name fairly upon the paper and "now I was a soldier, in name at least, if not in practice."

This also shows us a little bit about how recruitment was actually done. There were a handful of more or less permanent recruitment offices. Samuel Nichols, the commander of the American marines, maintained an office throughout the war to recruit marines, and larger cities like Boston and Philadelphia maintained active recruitment stations as they could. But for the most part, recruitment was done as a sort of traveling show. An officer with a couple of senior non-commissioned officers would roll into town with a drummer and piper, play patriotic tunes as they marched down the street, and then set up shop at a convenient public place, usually on or near the commons or at a public house. As Martin described, the drum itself would become a sort of table and stage to display the cash bounties and sometimes even as a surface on which recruits could sign the articles. At various times during the war the enlistment bonus was increased to far more than the dollar that stirred the seeds of courage in young Martin - this became a problem for long-term veterans after a few years, because some of the enlistment bonuses were more than the already-enlisted soldiers were paid, and were especially hard to take when enlistment bonuses were handed to new soldiers and the veterans had their pay in arrears for years - but the promise of cash, right there and then, was a strong part of recruitment.

There's also a class element to recruitment. In a world where the political ideas were rooted in the community, the militia was looked upon as the more patriotic, balanced, laudable service, and the regulars were shifty, untrustworthy mercenaries who had to be motivated by pay. Rhetorical attacks against the British regulars often included the idea that the British regulars were automatons who had been beaten into inhuman mechanical killers. To become a soldier was in some sense to surrender one's humanity for money. In this sense, it tended to be the young and impressionable - like Martin, who, remember, had a great anxiety over convincing his grandparents to give their permission for him to join - or the desperate or greedy. In later American conflicts, like the '98 crisis, when word got out that an army was being formed for a possible war with France, the secretary of the army's desk was flooded with hundreds of applications for the officer positions, but recruiting the enlisted men only ever attracted dozens.

And we should bear in mind that though the American Continental Army was molded into a very competent fighting force, the vast majority of fighting on both sides was done by militia. Patriot and Loyalist militias could embody quickly for a purpose and disband just as quickly, and their presence could make the difference in critical battles, such as at Saratoga, which is probably the rhetorical high point of the "minuteman" ideal.

So in answer to your last question, no, soldiering was not looked at as just another job. It was simultaneously a patriotic, adventuresome burden to bear for posterity and a righteous cause, and also an alluring, dangerous threat to the soul. The course of the War for Independence provided many different opportunities for men to serve, in violent capacities as well as non-violent, and joining up with the regulars was definitely not the only way to do so.

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I highly recommend reading Joseph Plumb Martin's memoir, it is a highly entertaining and emotional perspective on the conflict that's brimming with detail.

I also think you'd enjoy the classic work by Charles Royster, A Revolutionary People At War