It is OK to enter on a tourist visa based on the statements in your question.
To activate H1B status, you will need to enter the U.S. with an H1B visa.
If you qualify for a B-1/B-2, the H-1B would not render you ineligible to come as a visitor.
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As long as you have a valid tourist visa, and can successfully demonstrate that your trip is temporary, it is fine to travel.
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