Do I owe U.S. tax on income I earned in my home country before I arrived?

Generally no. As a new resident alien, U.S. worldwide-income taxation typically begins on your residency starting date—not retroactively to the start of the calendar year. Income you earned abroad before that date is usually outside the U.S. net, which is one reason the residency start date matters so much in an arrival year. The portion of the year before you became a resident is treated as your nonresident period, so only U.S.-source income from that stretch is taxable here. There are nuances: if you elect full-year resident treatment to file jointly, you may pull pre-arrival worldwide income into the U.S. return, with the Foreign Tax Credit available to offset foreign taxes. Pin down your exact residency start date and keep records separating pre-arrival foreign earnings, since that line controls what the IRS can tax.