Hamilton has not driven the 2020 car since the end of testing in February.
Mercedes technical director James Allison said they worked on getting developments designed in January, February and March on to the car.
“We got a lot of ideas how to make it quicker. We hope to have a chunk of that for the first race,” Allison said.
All F1 teams were shut down from the last week of March through April and May, and returned to work this month in preparation for the start of the season in Austria on 3-5 July.
The number of upgrades they have managed to produce in that time will have a defining effect on competitiveness as the season starts up.
Allison said that the car launched in February was fixed at around Christmas, with the first part of this year spent designing upgrades.
“Quite a lot of those ideas were already in process through the design office before we were forced to shut down,” he said.
“Our challenge now is to make sure that quarter of a year of development can get off the drawing boards and onto the car as swiftly as possible.”
Mercedes tested at Silverstone last week with a 2018 car to give the team and drivers a chance to “blow off the cobwebs” and try out the new working practices aimed at avoiding any risks with coronavirus.
“Probably the biggest change for all of us is going to be being at a race weekend where there are no fans,” said Allison, who was talking in a video published by Mercedes.
“That is going to be a very strange experience. It’s normally one of the pleasures of being at a track.
“I’m itching to find out in the crucible of a race event whether the work we did has produced a car we can be excited and proud of.”