Yes, but if He told the thief “today” but hadn’t gone to the Father until two/three days later (and, assuming from that, heaven), then where is this paradise the thief was going to be with Him at? It appears somewhere different from where the Father is.
The thief’s soul went to Paradise on Good Friday evening, as soon as he expired. Christ’s soul went to hell, where among other things, He actually defeated satan, stripped him of all power and authority and took from him the keys of Hell and Death. Then on Sunday morning, He arose. There is a lot more detail, but no need swamping you. Trust Christ as your Savior, and THEN learn more details
Paradise and Hell were in the same place, separated by “a great gulf”. Heaven was not opened yet; until Christ took His blood up; etc. When Christ arose, so did long dead Jewish believers, and people recognized them. Then when Christ took the Blood to Heaven, He took the risen saints with Him. It’s all in the Crucifixion/Resurrection accounts in several Gospels. Read it.