I did a keyword search for “baptized” and here are all the scriptures. As you can see, there is an order to baptism - no one is to be baptized until they believe. This is stated strongly by Peter in Acts 8:36-38.
Acts 16 reads that the entire household believed.
He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Acts 2:37-38, 41
Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.
But when they believed Philip preaching the things concerning the kingdom of God, and the name of Jesus Christ, they were baptized, both men and women.
Then Simon himself believed also: and when he was baptized, he continued with Philip, and wondered, beholding the miracles and signs which were done.
And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.
(Saul (Paul) believed, regained his sight, received the Holy Spirit, and then was baptized.)
(Peter preaching to Jews and Gentiles, those who heard the Word believed, the Holy Spirit fell on them, then Peter told them to go and be baptized.)
But Paul cried with a loud voice, saying, Do thyself no harm: for we are all here.
Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas,
And brought them out, and said, Sirs, what must I do to be saved?
And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
And they spake unto him the word of the Lord, and to all that were in his house.
And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway.
And when he had brought them into his house, he set meat before them, and rejoiced, **believing in God with all his house. **,
And Crispus, the chief ruler of the synagogue, believed on the Lord with all his house; and many of the Corinthians hearing believed, and were baptized.
And he said unto them, Unto what then were ye baptized? And they said, Unto John’s baptism.
Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
When they heard this, they were baptized in the name of the Lord Jesus.
In my opinion, it would be too far a stretch to consider the Great Commission as including infants. “Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost”. To say that includes everyone, including infants would be saying atheist are included too. What good is baptism without belief? I think scripture is clear - believe, then be baptized.