Yes, there is a cost basis. Your employer should have included the value of the stock on the day you received it in your taxable income. That amount will be included in box 1 of your W-2 for the year you received it. Your employer may have noted the amount in box 14 of your W-2. Since you have/will pay tax on the value, your cost basis is that value.
If I don’t have the W2 for that tax year, is there another way to figure out the cost basis?
Reach out to your employer or payroll company to see if you can get a copy. If you happened to mail your w2 to the IRS that year, you can pay them for a copy.
If you can't show a basis, the IRS values it as zero so you pay tax on the full amount.
I want to urge you to create a financial notebook that is kept separate from your tax return. Keep it safe and each year, add your year-end statements from all your financial accounts plus a copy of your W2’s, your carryover information, and proof of your basis in your various investments. You must keep tax records from the time you purchase until sold/ loss used plus 3 years. It is very easy to lose track of disallowed losses, carryforwards, and basis.
This can be a digital or paper notebook.