From what I remember when I did the Project One build I didn’t have the option. I have the Fox SC 100 on my hard tail, so could have swapped it over but after getting the SID Ultimate tuned I’m happy with it now. It looks like this year you can get a Fox Performance fork, and it drops $500 of the build, but not the Fox Factory fork. The Fox Performance was an option when I built mine.
With Project One it’s not always as customizable as you would think it should be. I went Eagle AXS and this also forced me to choose SRAM Guide brakes. I worked a deal with the shop to swap those out for Shimano XTR brakes. I am used to the XTR brakes as I have them on my other bikes. The shop did this at no charge, but we did work the details out before I ordered the bike.