Answer: Yes, a U.S. citizen son can petition for his father’s Green Card. The process normally takes a year/year and a half.
A U.S. citizen brother can petition for his brother’s Green Card as well. The process for most countries normally takes about 15 years. It could be longer for people born in some countries (Mexico and Philippines).
You can start the immigration process even now during COVID-19 pandemic because the USCIS Service Centers are still open.
However, in order to complete the immigration process, a U.S. citizen petitioner will have to move back to USA or prove that he has immediate plans to relocate back to USA. It is also important to show that a U.S. citizen petitioner filed his tax returns with IRS, which would be required at the last stage in the immigration process for the Affidavit of Support.