Yes, first and reverse are not syncronized but they are still operated by a shift fork on the side cover. The L/R slider gear slides on the outer sleeve of the syncronizer drum and either engages the low gear on the cluster gear or the reverse idler which is on a separate shaft in the case. In this situation it is more than likely a clutch related problem.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine