Put yourself in the hiring manager / HR shoes of the new company.

Unless they were aware beforehand that you're interviewing with another company and expecting an offer from them, it's going to look bad on you.

You accepted their offer with no caveat.

If I was the hiring manager, I would 100% not accept a negotiation for increment on bad faith, and depending if I could get another candidate, I will even push HR to retract the offer.