Not necessarily as the Holy Spirit was only shown to be given first a couple of times, other times it was not given tell later.
To say that everybody gets the Holy Spirit before water baptized is not true by the scriptures. The Lord can administer the Holy Spirit to a believer at anytime in their walk in the faith.
Peter shows that in Acts 2:38 as he is telling those there to repent and be baptized to receive mission of sins, then he says after that they will received the Holy Spirit. Showing those in Acts 2:38 were baptized in water first, and repented before they received the Holy Spirit.
The other thing you need to get away from is saying my old Roman roots, as the Catholic church that I was in for 5 years did not teach me. As a matter of fact they taught very little scriptural in studies, mostly history.
My studies come from personal studies, and online biblical schooling from biblical scholars.......
Then you have Peter saying this, not me;
1 Peter 3:20-21
20 who formerly were disobedient, when once the Divine longsuffering waited[a]in the days of Noah, while the ark was being prepared, in which a few, that is, eight souls, were saved through water. 21 There is also an antitype which now saves us—baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ,
( This here is the same baptism mention in Matthew 28:19, Mark 16:16, Acts 2:38, and Acts 10:47 )