OP doesn't appear to want to run any new wire. Switching after the GFCI would require new wire. Swapping in a breaker solves this problem. However not being an electrician I don't know if swapping in a GFCI breaker could cause any other issues.

Given that OP is asking such a question I definitely wouldn't recommend they swap a breaker. They should 100% contact an electrician.

Edit: Just realized what you were getting at. Assuming OP could find an outlet that comes before the switch/outlet combo he could 100% swap that with a GFCI outlet. Again given the way this question is being asked with no additional information OP should call an electrician.