[RPG] Is it fair to press the players for decisions during combat

Give them a few options, with the last one being "or do something else."

Your players are a group of people with other stuff they're thinking about who are simultaneously socializing with each other as players and trying to play a game. They don't have the story and setting in their heads like you do, so you're doing them a favor by exposing your view of their goals and approaches to them.

When I GM, I find it effective to periodically say things like "So it sounds like your plan is to either do X or do Y," or "At this point you could do A, do B, do C, or do something else." Think of your campaign as a choose-your-own-adventure game where there's always an "other" option that's picked half of the time.

You can also simply reiterate their goals and their situation: "So. You know that you need to find the Foo. You're currently in a Blah room and there are two doors you haven't explored." Since you have hesitant players, you can just pick one who hasn't contributed in a while and say, "Sue. What are you doing?"

When the players are hesitant, the GM can always describe the situation, list the immediate options (leaving an "other" option to avoid railroading!), and pick someone to put on the spot. In the worst case, another player will come to their rescue and perform an action to get the plot moving.

This is where a "living world" pays off.

When designing the adventure (guardian/first encounter + dungeon, as you describe it) you'd intended that the party should tackle the first encounter, then go on to the dungeon. You expected your players to go with this plan, based on their previous behavior, but you don't mention any reason that the characters would press on.

So why would they? What was the in-game reason that the characters should run-not-jog, bleeding, from the first encounter into the dangerous dungeon?

Maybe you left that part out. Maybe you put it in, but it wasn't well understood by the players. These things happen.

Keep your living world front-and-center.

Assuming you've come up with some in-fiction reason(s) that the party should want to advance along your expected timetable, go ahead and reinforce this all the time. When I'm running campaigns^* I use a mashup of a "plot advancement w/out party" chart and a dungeon-world front sheet to keep my eye on the ball. (Literally: when I'm running homebrew it's not statblocks sitting in front of me on the table: it's my front-sheet, a mind-map of connected persons/places/events, and notepaper.)

In your example it might be as simple as "the McGuffin-on-a-timer is in the dungeon." Let's run with that.

Once you have a sense of how the world is going to run if the PCs don't intervene, keep dropping info/hints/pointers to later elements in the chart: someone's power is fading because of the continuing McGuffin, or an NPC checks back frequently to see how the quest is going, a "random" encountered enemy turns out to have been on the same trail, &c. It's only fair to expect the party to go do the thing if they know it's there to be done.

Secondly, when the party misses something in the chart, refer back to it. With some frequency. Your party bypassed the dungeon and went to town. The next day when they're on the way to the dungeon let them pass their rivals coming back, loaded with treasure. Or let the threat have grown worse. Or let it have moved. Just be sure the players know that yesterday they could have had this adventure, and they knew it, but they passed on it.

^{* - homebrew campaigns, at least; I'm finding recently in published adventures I'm not motivated to do all the "extra" work it takes to layer this onto someone else's material.}