Opus 17 is incorrect in stating that this can only be a contribution for 2023. As long as when the employer made the deposit the employer informed the plan that this was to be a contribution for 2022, it's a contribution for 2022. This would be indicated by the $300 being present in box 3 of your 2022 Form 5498-SA from the HSA custodian.
Assuming that this was correctly deposited as a contribution for 2022, when completing the HSA section in 2023 TurboTax you'll indicate that the employer "told you about other contributions" and enter $300 in the box identified as being for contributions for 2022 made in 2023.
Note that this $300 should also have been included on your 2022 Form 8889 by indicating in 2022 TurboTax that "your employer told you about other contributions and also entered as a contribution for 2022 made in 2023.
