What do you mean "apply for taxes"?
If you mean can you complete and file a 2024 tax return in June, then the answer is Yes.
You can complete and e-file a 2024 tax return using TurboTax up through October `5, 2025.
Go to this TurboTax website to start a 2024 online tax return - https://turbotax.intuit.com/personal-taxes/online/#diy