This method looks very interesting and fun.

https://fate-srd.com/odds-ends/elective-action-order

I especially like how it creates a level of tactics in keeping control of the conflict.

I’d emphasize that, however we do it, initiative order can be modified and/or controlled through stunts and/or expenditure of fate points. So, if you really want to go before the other guy, be prepared to spend / invest / bid more than him on going first.