As a college student I was an assistant coach for a travel team earning 1405.00 in 2021 and was issued a 1099-NEC, do I need to claim this?

Yes, you need to include the NEC in your tax return. Since it is not intended to be your full time income for living - like a business, it can be reported as other income on your return instead of a sch C.

If you have no other income, entering it as "other income", is the simple solution.  

After entering the 1099-NEC, the next screen will be "Does one of these uncommon situations apply".  At that screen, check the box "This is not money earned as an employee......."

Expect to pay about $30 federal income tax.