Do not present a timer, make it part of what motivates the player.
You are in space with an astronaut - where air is scarce and CO2 needs to be recycled. For that to happen (solar) energy is needed to work the ductwork and provide for the apparatous that removes CO2 / pumps O2 / works the repair drones for ship maintenance.
the astronaut uses air up: the available O2 storage is slowly decreasing - this provides a slow sense of urgency
rising CO2 levels will make breathing impossible when ever they reach a certain threshold the air simply is not breathable anymore (real danger)
energy may be sparse due to malfunctions of solar sails, being shadowed by a moon, malfunctioning energy lines, ...
sometimes bad things happen:
- microastroids puncture sections, they drain of O2 before shut off
- malfunctions of the CO2 regenerators: CO2 removal is decreased
- contamination: septic line broke, that part of the ship is now poisoned unless cleared
- electricity shortage due to shadow, malfunction, arcing where it should not, solar sail gets punctured, ...
sometimes good things happen:
- you stumble over an unused O2 container
- solar sails got cleaned by solar winds and work more efficiently
- you are able to deploy some emergency sails
- rerouting energy through those other handwavium paths circumvents burned out sections and more energy reaches the areas it is needed
- you are able to fiddle some rescue capsule battery into your stations system for a boost of energy
- scrubbing the CO2 algae clearing tanks makes them work 110% for some limited time
- a O2 bubble flashes over the puzzle and the player clicks it for some O2 gain
- you defrost your favorite plant and it helps you with CO2->O2 conversion
- you find the prototype of a new kind of spacesuit that has build in recycling capabilities
- certain things might be beneficial (solar eruption -> more energy from solar sails) but on the other hand averse (damages the hydroponic - so less CO2 conversion)
- ...
You got multiple ways to further / diminish urgency - some of them by dropping random O2 bubbles or CO2 cleanups on the player to click it. You can have puzzles related to fixing equipment, gather resources. You can have random events that influence any one of the 3 angles for time pressure - you can even have the player choose: is it better to take the puzzle to get the energy rerouted or to search this darkened section for O2 canisters.
The player needs to balance the 3 things (O2, CO2, Energy) between certain min/max levels and chooses puzzles accordingly - if things get out of those areas change up the game mechanics:
Low energy leads to dimmer / fluctuating lighted screens, low oxygen tints everything in red and makes things on the borders of the screen blurry and wavy. Too much CO2 makes the mouse react sluggish (0.1s) and sometimes needs a second/third click to make things work.
Nothing major - just some influence is enough.