If the employer has an HSA set up then ask them if they will make the contribution if you are eligible. If you do not make the contribution thru the employer/payroll system and you have not maxed out the contribution limit yet this year then you have until 4/15 to make a prior year contribution to an HSA.
It doesn't matter where the money comes from. If you are eligible to contribute to an HSA and have not already contributed the maximum, you can contribute additional amounts up to the maximum annual limit for your type of coverage. The contribution does not have to be made through your employer. If the particular HSA that you have doesn't permit contributions other than those deposited by your employer, you can always open another HSA and contribute to that to make up the difference. All of an individual's HSAs are treated as if they were a single HSA.
In short, yes, you may make a lump sum out of pocket contribution. The deadline to be counted as a 2020 deduction is April 15, 2021, but you must tell the HSA bank that this is a 2020 contribution and not a 2021 contribution before you make it. And, you must keep to the overall contribution limits for 2020, depending on how many months you were eligible and whether you are covered by a single or family HDHP.