Whenever the American Revolution comes up it seems like a large portion of the American military leadership made their bones in the French and Indian War.
How big a part did that war play in the Revolution? Would the Revolution have been possible without the combat experience of the prior war?
Yes, a significant number of the Continental generals in the Revolutionary War got their start in the Seven Years War. Not only Washington, but Horatio Gates, Charles Lee, and Daniel Morgan, as well as other officers, like colonels William Crawford and Hugh Stephenson. That many of them were Virginians is not accidental: it was Virginia governor Thomas Dinwiddie who would vigorously push Virginia claims into French territory, and create the Virginia Regiment to oppose the French when the war started. The Virginia Regiment was not very effective in asserting Virginia's claims: until the advent of a large professional army under Amherst in 1758, the French were largely successful in dealing with the colonists. But Washington would learn how to keep a poorly-equipped sporadically-funded force in the field and avoid disaster, as well as how to negotiate- and beg- from a political leadership that was very infirm of purpose. Those skills would be crucial to his later success in the Revolutionary War.
Of course, not every British officer who was in the French and Indian War joined the Continentals: some would become Loyalists. General Thomas Gage would be Washington's opponent.
But the French and Indian War would also be a primal cause of the Revolutionary War. It gave Britain a huge amount of new Canadian territory to administer, and the failure of the colonists' own militias against the French demonstrated a need for a standing army there. The costs of doing all that were put onto the colonists, and they resented it. The French and Indian War was also sparked by the colonists' desire for more land. Dinwiddie granted western lands to the veterans of the Virginia Regiment in reward for their services. That turned out to be premature: the Proclamation of 1763 drew a line for western expansion of the colonies at the Alleghenies, and though the 1768 Treaty of Fort Stanwyx with the Iroquois granted some lands for settlement, it was much less than the colonists had hoped to get. One of the Virginia Regiment's disappointed officers hoping for land was, of course, George Washington.