Can we deduct downpayment that we paid in 2020 for a house that didn't require the first mortgage payment until January 2021?

No.  Down payments for a purchase of a personal residence are not reported on nor deductible on a tax return.

No, your down payment is not deductible.

Home Ownership

There is not a first time home buyers credit on a Federal return. That ended in 2010. If your state has such as credit, you will be able to enter it when you prepare your state return.

Buying a home is not a guarantee of a big refund.  Your deductions for homeownership combined with your other deductions (if any) must exceed your standard deduction to change your tax due or refund. If you purchased your home late in the year, you do not even have a full year of home 

ownership deductions.

Your closing costs on your new home are not deductible except for prepaid interest, prepaid property tax or loan origination fees.  There are no deductions for appraisal, inspections, title searches, settlement fees. etc.

Your down payment is not deductible.

Your homeowners insurance for fire, hazard, flood, etc. is not deductible for your own home.

Home improvements, repairs, maintenance, etc. for your own home are not deductible.  

Homeowners Association  (HOA) fees for your own home are not deductible.

If you pre-paid any of these expenses you can enter them in

Federal> Deductions and Credits> Your Home:

Mortgage interest, property taxes, private mortgage insurance (PMI) and loan origination fees (“points”) that you paid in 2020.  

HOMEOWNERSHIP DEDUCTIONS

It is very hard for a lot of people to use itemized deductions now that the standard deduction is so much higher.  Your home ownership may not have any effect on your tax due or refund, especially if you purchased the house late in the year.  

Standard Deduction
Your itemized deductions have to be more than your standard deduction before you will see a change in your tax owed or tax refund.  The deductions you enter do not necessarily count “dollar for dollar;” many of them are subject to meeting  tough thresholds—medical expenses, for example, must meet a threshold that is pretty hard to reach.  The software program uses all the IRS rules that apply to the expenses you enter, and it tells you if you have enough to use your itemized deductions or if using the standard deduction is more advantageous for you.  Under the new tax laws, some deductions have been capped—there is a $10,000 limit to the itemized deductions for state, local, property and sales taxes. 

2020 Standard Deduction Amounts

Single $12,400   (+ $1650 65 or older)

Married Filing Separate  $12,400   (+ $1300 if 65 or older)

Married Filing Jointly $24,800   (+ $1300 for each spouse 65 or older)

Head of Household $18,650  (+ $1650 for 65 or older)

Almost nothing is deductible.  You never deduct your downpayment -- that's your investment in the property.  Money deposited in escrow is not deductible until it is actually spent for a deductible expense like real estate taxes, because until then it is still your money.

You probably paid daily interest from the closing date to the last date of the month.  That will be reflected on your closing statement and may not be included in your 1098 from your lender, if not included, you can deduct it separately. 

You can deduct property taxes paid on your ownership period in the home, including a credit you gave the seller, as if you paid it to the taxing authority.  For example, if you closed November 29 and your property taxes are billed January 1-December 31, you probably paid the seller a credit for 33 days of property taxes for the period of time you owned the home, which the seller paid in advance at the beginning of the year.  You can deduct those taxes as if you paid the taxing authority directly.  

You can deduct "points" on your mortgage if you paid them and meet the tests required by the IRS.  Turbotax will ask about points. 

You can deduct mortgage insurance if you paid an up-front premium (PMI, MIP).  This must be spread out over the life of the loan or 84 months, whichever is shorter, so if you closed in November you can deduct 1/84th the lump sum PMI.  (If you paid an FHA rural funding fee or VA funding fee, that is deductible in full when you close.). The mortgage insurance deduction is subject to an income limitation so not everyone will qualify.

Your other closing costs are not deductible, but some of them can be added to the cost of your home and may reduce your capital gains when you sell.  See the list in publication 523.

https://www.irs.gov/pub/irs-pdf/p523.pdf