Since Timekeeper says Gingerbrave was a meaningless variable in the future, let's speculate what the world would be like if Gingerbrave was gone.
For this I will be talking about Kingdom's events because Gingerbrave hardly does anything in OB, he just runs out of the oven and meets a bunch of randos.
Let's talk Kingdom events: Without Gingerbrave;
The sugar gnomes would be in a bit of a pickle with the cookies of darkness bringing monsters there. The cookies of darkness would have the crown the cake hound grabbed and we don't know what the crown does so we don't know what that means.
Dark Enchantress would possibly still be trapped in the moonstone, since Gingerbrave and the squad broke the stone.
Pure Vanilla would still be Healer cookie, since there is no inciting incident Gingerbrave brings to get him to figure his stuff out.
The Hollyberry Kingdom events would still happen, Gingerbrave doesn't to anything in the main story.
The Dark Cacao Kingdom events might still play out, there is just no letter being brought to Dark Cacao.
Golden cheese would still be in her perfect golden paradise, since Gingerbrave wouldn't bring the errors into the world. Olive and Adventurer could still enter the virtual world but there would be no war incoming to force her to wake up.
The council of heroes wouldn't happen; which also means no magic candies, incoming war, attack on the republic, etc.
The events of Beast Yeast might still happen, just slightly different.
This is all assuming the Cookies of Darkness DON'T find a way to break the Moonstone. With no Gingerbrave bringing the warning cry and the mysterious crown in her hands, the cookie world wouldn't see Dark Enchantress coming.
So Timekeeper, he may be insignificant in OB but holy crap we'd all be dead without him in Kingdom.