In Judea when Jesus walked the Earth burial was being placed in a tomb without any dirt being thrown on top. Just roll the stone away and walk in and out after the resurrection. Do you remember the story of Lazarus, brother of Mary and Martha? He was placed in his tomb and when the Lord Jesus Christ called to him he came out of it without being covered by dirt. He was however, covered in burial cloth. Nothing to suggest submersion in that. But it appears you're thinking of Romans 6. That passage says:
What should we say then? Should we remain in sin so that grace may be given the more fully? Out of the question! We have died to sin; how could we go on living in it? You cannot have forgotten that all of us, when we were baptised into Christ Jesus, were baptised into his death. So by our baptism into his death we were buried with him, so that as Christ was raised from the dead by the Father's glorious power, we too should begin living a new life. If we have been joined to him by dying a death like his, so we shall be by a resurrection like his; realising that our former self was crucified with him, so that the self which belonged to sin should be destroyed and we should be freed from the slavery of sin.
(Romans 6:1-6)
No submersion in that passage is there? But there is an explanation of baptism in it. The passages teaches that in baptism one is united to Christ. It teaches that one dies and rises with Christ when baptised. That is nothing like the anaemic explanation you've given in your posts. You say baptism is a public testimony about your commitment to faith in Jesus Christ but saint Paul says it is death and resurrection with Christ. It's the birth from above that Jesus mentions in the gospel according to saint John saying:
There was one of the Pharisees called Nicodemus, a leader of the Jews, who came to Jesus by night and said, 'Rabbi, we know that you have come from God as a teacher; for no one could perform the signs that you do unless God were with him.' Jesus answered: In all truth I tell you, no one can see the kingdom of God without being born from above. Nicodemus said, 'How can anyone who is already old be born? Is it possible to go back into the womb again and be born?' Jesus replied: In all truth I tell you, no one can enter the kingdom of God without being born through water and the Spirit; what is born of human nature is human; what is born of the Spirit is spirit. Do not be surprised when I say: You must be born from above. The wind blows where it pleases; you can hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone who is born of the Spirit.
(John 3:1-8)
The reason for baptising infants is that infants need to be born from above just as much as grown up people do. And Jesus teaches that it is by baptism that one is born from above.