do you think peace between Britain and the colonies could have been possible before the Battle of Ticonderoga and the Battle of Bunker Hill?

Yes,  Lexington and Concord plus other early 1775 battles were skirmishes of colonists exerting their rights as British citizens.  As noted by several historians.  

Battles like Bunker Hill and Ticonderoga showed the militias could achieve some strategic and tactical victories, total independence gained momentum.  Plus King George III started enlarging the British army and navy to crush the rebellion.

Explanation:

Bunker Hill:  June 17, 1775

Revolutionary battle at Fort Ticonderoga:    May 10, 1775

Signing Declaration of Independence:  July 4, 1776.  Official document spelling out in written form what was already taking hold in mindsets of most colonists.

explanation:

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