a most incredible feeling
"....I started to get dizzy...and then I felt a certain peace." (The man was coughing.)

His eyes widened. "Mitch, it was a most incredible feeling...."

(from a book)
If I change 'a most incredible' to 'the most incredible', will it mean the same and sound natural?

Yes, that sounds fine to me.
We usually say "the most incredible", even though the superlative isn't actually true.