I'll give u the answer straight.

If u join corp banking as an assistant RM(associate) first, after a few years,
you'll have a good chance of becoming an RM.

If u join PB as an assistant RM aka RO, u will remain stuck in that role. 90% of ROs do not become private bankers simply because no bank will spoonfeed u with their high net worth clients portfolios. The minority who do so are either very lucky, or have proven themselves to be exceptional (for eg. by completing CFA and MFE, which RO rarely possess. Still it's not a guarantee u can switch to PB) You'll have a better chance of becoming PB if u work in banks as priority bankers first doing sales (1 tier lower than PB)

Lastly fyi, Senior corp bankers can switch to PB but not the other way around, reason being corp bankers have r/s with CFOs, CEOs, but private bankers have no relevant corp banking experience including credit analysis, transaction banking etc