Yes, switching to another legal status (H1B, GC) from TPS is allowed by the law if you find a sponsor and meet the criteria for that status, as long as you were NOT out of status for more than 6 months before you had TPS. It is written in USCIS literature and not a personal assumption.

You will not be allowed to adjust status for permanent residency without exiting the US for certain number of years (3-year bar or 10-year bar depending on how long you were OOS) if you were out of status before TPS.

More than 6 months but less than 1 year OOS = 3-year bar
More than a year OOS = 10-year bar