So, was Cornelius saved when he believed and was filled with the Holy Spirit, or later when he got wet?
“Yes.”
Your answer is ambiguous. So, which was it.
When he was filled with the Holy Spirit?
OR
when he got wet.
The bible says we are 'saved' by many elements that are all tied together and can't be isolated.
1 Peter 3:21 Baptism now saves you
Romans 10:10 Confession saves you
Ephesians 2:8 Grace saves you
and so on.
Each of these elements are part of the package deal.