Accepted a job offer and signed a contract. Got another offer that pays WAY more. Should I bother renegotiating w/ original employer?

Entering workforce for the first time. I really like the culture of Company 1 who extended an offer first and they treated me better throughout the recruitment process. It's been 2 weeks since I signed the contract. However, I held out for Company 2, who just offered me a salary that's 13k higher and a sign on bonus that's 8k more than what Company 1 offered me. I think I'm prepared to walk away if needed (have to sleep on it tho) but if I really would prefer to stay at Company 1, should I bother bringing it up? Or will that be too risky/hurt relations/etc.? If it's too much to ask for a salary increase now, could I ask them to write in my contract I want a salary increase in like 3 months after starting? 21k is not an insignificant number. -- if it was only a few thousand I'd probably let it go.

Company 1 and Company 2 are competitors and they likely lose employees to each other. I will probably only stay 2-3 years at either company, though that could change if I have a super positive experience. Someone recommended I go to Company 2 now and if I don't like it I can probably get into Company 1 later -- but is that unlikely to happen if I back out now?

*edit: both companies do management consulting

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