push ahead (with something)
To proceed or continue with some action, task, or activity, especially with determination or in the face of adversity. The start of my presentation did not go as I had hoped, but I had to just push ahead and keep talking. We need to push ahead and get back to camp before sunset. We decided to push ahead with the project despite our manager's departure.
push ahead
(with something) 1. Lit. to go on ahead, pushing with something. The worker pushed ahead with the plow, moving the snow to the side of the road. Our car followed the snowplow, which was pushing ahead at a fast clip.
2. and push ahead (on something) Fig. to continue to progress with something. Let's push ahead with this project immediately. I want to push ahead on this project.