You are a US resident for tax purposes starting on the day you arrive with your green card. As a US resident, you are required to report all your worldwide income and pay US tax on it. You can claim a deduction or credit for taxes paid in a foreign country on the same income.
If you file as a US resident for 2020, then all your worldwide income is US income for 2020, even money you earned in a foreign country before you got your green card. You get the same tax deduction or credit for foreign taxes paid. To avoid this situation, you file as a dual-status taxpayer for 2020. As a dual-status alien, you still pay US tax on all your worldwide income earned when you were a US resident, but you only have to pay US tax on your non-resident income if it was from a US source. (If all your income before becoming a US resident was non-US, you would owe no tax on that.
Filing as a dual-status alien is not supported in Turbotax. See the IRS web site for more information.
https://www.irs.gov/individuals/international-taxpayers/taxation-of-dual-status-aliens
It appears that you will file form 1040 (a regular US tax return). You would only include your income starting on the date you become a US resident (both US and foreign income). You can't e-file, you must file by mail and write "Dual status alien" on the top, and attach a written statement showing any US income and tax owed from US income when you were a non-resident. (If you did not have US source income when you were not a resident, you can just say so.) But there appear to be some additional limitations and rules for filing the part of the return that covers your US residency. See the IRS or a tax professional for more assistance.
