You can apply with the USCIS to transfer your H1 visa to a new employer.Quoting pruthvi
You may not enter the U.S. on the basis of an H1 visa where you have no actual employment. If you enter as a tourist, you would not be entitled to overstay your tourist visa. To stay you would need to otherwise gain lawful immigration status, which of course might not happen within the necessary timeframe through your prospective H1 employer.Quoting pruthvi
You may benefit from discussing your situation in detail with an immigration attorney.

