You guys pass the Green Card Test for 2021, so you are resident aliens for 2021, but since it's your first year of residency, your residency starting date is when you became a permanent resident (December 31), so you would be by default dual-status for 2021 -- resident for the last day, and nonresident for the first 364 days. Residents are taxed on their worldwide income, while nonresidents are taxed on only their US income. If you didn't have US income for the first 364 days, and didn't have worldwide income for the last day, neither of you would be required to file a 2021 tax return. Note that even if you did file, you would file as Married Filing Separately -- dual-status cannot file jointly. You would each file form 1040 with "Dual-Status Return" written across the top, you cannot claim the standard deduction, and you would each attach a 1040NR or other statement showing your US income for the part of the year you were nonresident.
Since you are married, and you were residents on the last day, you could elect to be treated as residents for the whole year, and file jointly. But seeing as you don't have income taxable by the US while filing separately, there isn't any benefit to filing jointly, and treating yourselves as residents for the whole year subject your worldwide income that year to US taxes, and you could probably use Foreign Earned Income Exclusion to exclude taxes from that income, but it's still a pain to report that income and claim the exclusion, when there is no benefit.
One interesting issue is the third stimulus payment ($1400 per person). If you were a resident alien for 2021, had a Social Security Number issued before the due date for 2021 taxes, including extensions (the regular due date was April 18, 2022; if you had extension the deadline is in October), and your income was below a certain level, then you can each claim $1400 in Recovery Rebate Credit on your 2021 tax return. If you can claim this, then it would be worthwhile to file just to claim this.
