No. It’s the other way around
What builds credit is a stream of timely payments. Since 90% of your Fico score is determined by last 24 months activity, you actually need your credit report to show 24 timely payments dating 2 years back.
Paying student loans or installment loans builds credit over time. Paying off the loan does nothing special for your credit/score. The paid-off loan becomes a closed/paid account in good standing which looks good on your credit report but does not count as much in your score as opposed to open, active lines of credit.
If you made at least 24 payments then your score should be between 660/749 which is a good score (assuming you have no negatives on your credit report).
The only positive side of paying off the loan is that you can save a lot of interest if you do. Sometimes it’s smarter to think with your pocketbook and not worry about your score, although having a good score can save you money if you plan to take a car loan or a mortgage.