Minecraft Java Edition – Can Mobs Use Levers?

The words compact and Redstone don't usually go together :) There could be something simpler than this, probably using some weird combination of water, pistons, and chewing gum, but this is the best I can come up with: a basic delay circuit (from the wiki):

In the screenshot, there is actually a pressure plate on the right, bit hard to see. I prefer not to use buttons, when running for my life. :)

I would suggest using buttons instead of switches. You push a button, the door opens, then the button deactivates, closing the door.
It's true that the delay is really short, maybe not even enough for you to get through. This problem can be solved using repeaters to build circuit delaying the closing signal. I currently don't have enough time to try and build a working solution, but if you won't figure it out on your own by then, I'll do my best to update this post later in the day.

Edit: Just for for the sake completeness: instead of buttons, you could also use pressure plates. Just place one in front of the door from both sides. Be wary though, because mobs can also trigger them. (I almost lost my mind once, when I had a door wired like this and a damn chicken kept stepping on the plate and banging with the door. I had to replace the plate with a button.)