The SNP minister said the vaccine programme is now "exceeding expectations" after the daily number of jabs ramped up dramatically last week.
The country is now on course to inoculate all over 70s and clinically vulnerable groups over the next week, in line with a flagship target, as well as vaccinating all over 50s by May.
Ms Freeman said the programme would then look at when to start vaccinating under 50s, alongside dispensing second doses to older groups
"In effect from the end of this month, early March, we will be running two vaccination workstreams - the second doses vaccination, for all those who have had their first dose, and continuing the first dose,” she told BBC Scotland’s Sunday Show today.
"If supplies allow us to to do that then we should meet all those projected completion dates."
Ms Freeman said that the Government is waiting on advice from the JCVI (joint committee on vaccine and immunisation) on how to proceed with under 50s.
"We should know that fairly soon and at that point we will make our decision about what we do once we have vaccinated everyone over 50."
Asked if there was a scenario where all Scots adults could be vaccinated over the Summer, Ms Freeman said: "Absolutely, there is a scenario."
But she insisted this would be down to supplies.
"Our ambition is to get through 4.4 -4.5 million adults aged 18 and over in the Summer," she added.
"At this point it is not very sensible to give specific dates because there are a number of unknowns."
But she added: "What is the case is that our infrastructure to do that is there. We have vaccinators, we have support staff, we have the local and the regional centres.
"So we just keep going. As fast as we get supplies, we will be vaccinating."
Ms Freeman refused to speculate on when restrictions could start to be eased allowing a return to normality, but said numbers would need to sink to the lowest level possible.