Paul's letters are dated between 50 and 58 CE.
The first gospel is that of Mark, c. 75 CE, datable by its mention ("prediction") of the sack of Jerusalem 70 CE, and by its author's use of Josephus' report of the trial of Jesus son of Ananias in Wars, published 75 CE, as the template for Mark's trial scene of Jesus. Matthew and Luke borrow passages wholesale from Mark, hence are later, mid 80s. And John is last, mid or late 90s.
To me the first Gospel is that of Matthew. First because first it was written in Hebrew shortly after Jesus died.
Whereas, Mark wrote in the 60's with the non-Jews in mind. Luke wrote in the 50's. Yes, John late 90's.
Paul's 'earlier' writings do reference Matthew, so Matthew could have been available to Paul.
for example:
1 Corinthians 15:3-4 matches Matthew 28:6
1 Corinthians 10:16; 1 Corinthians 11:23-26 matches Matthew 26:26
1 Corinthians 16:13; 1 Thessalonians 5:6 matches Matthew 26:38
1 Thessalonians 5:6 matches Matthew 25:13
2 Thessalonians 2:3-7; 2 Corinthians 6:14 Matches Matthew 24:12
1 Thessalonians 5:1-2 matches Matthew 24:36
1 Thessalonians 5:2 matches Matthew 24:43
2 Corinthians 1:7 matches Matthew 20:23
1 Corinthians 3:5-7; 2 Corinthians 1:24 matches Matthew 20:26
1 Corinthians 7:7 matches Matthew 19:11
1 Corinthians 7:32, 38; 1 Corinthians 9:5 matches Matthew 19:12
1 Corinthians 6:2 matches Matthew 19:28
1 Corinthians 5:1-5,11-13 matches Matthew 18:17
1 Corinthians 10:32; 2 Corinthians 6:3 matches Matthew 17:27
1 Corinthians 10:4; 1 Corinthians 3:11; 1 Corinthians 1:2 matches Matthew 16:18
1 Corinthians 2:1,9 matches Matthew 13:11
2 Corinthians 10:1 matches Matthew 11:29