I'm negotiating a project as a contractor Software Engineer (sole proprietor) and wonder if I can (I should) recognize the income this year if the company is willing to pay for the part of the project in advance this year?
If you are cash based ( not accrual) then all income received during the year is taxed income in that tax year so if they pay you some in 2021 you report it in 2021 even if you have no expenses to report on that job. It is up to you to decide what is in your best interest ... seek local assistance in how to set up your books and run a business ... education is key to your success.
You are a cash basis taxpayer and you record income when it is actually paid and expenses when you actually pay them, unless you go out of your way to set up an accrual system. This is complicated to do and not easy to reverse if you change your mind. You need expert assistance if you want to change your business accounting method.
If you run your business using accrual based accounting, you recognize income when the work is performed. But also note, this would mean that if you completed a job on December 31, you would recognize the income in 2021, even if the company doesn't pay for 90 days, well into 2022. You would have to pay your income tax before you actually get the money. It's not a simple decision to make.
cases involving accrual basis taxpayers
Automobile Club of Mich. vs. Comm. 353 US 180 (1957)
Membership dues received one year in advance by an automobile club were includible in income in the year received by an accrual basis taxpayer because the dues were held under a claim of right without restriction of their disposition.
Comm. vs. Indianapolis Power & Light Co. 110 S. Ct. 589 (1990)
The U.S. Supreme Court made a distinction between the taxation of refundable deposits. The Court confirmed advance payments are generally taxable and defined "advance payments" as a non-refundable payment. With a nonrefundable payment the payee is "guaranteed" it can keep the money as long as the payee performs its own obligation under the contract.
Schlude vs. Comm. 372 US 128 (1993)
Prepaid lesson fees were includible in income by an accrual-basis dance studio in the year of receipt and not pro rata over the period during which the lessons were to be given. However, contract installments not becoming due and payable during the year (and not secured by note) were not taxable in that year if the lessons had not yet been given.