I'm a relative new GM who only run a 2 years long heavily railroaded fantasy campaign that went south for various problems and that I decided to drop.
Now I started to run a sci-fi sandbox campaign (system is Mongoose Traveller) and so far we had few sessions and my players are enjoining it.
Until now I followed the main backstory of two of my players' characters: the search of the lost sister of one of them, loved by the other PC.
Their motivation the strongest in the party: another PC has no real motivations and the last has a long term and we could say "easy" motivation (founding outposts of his secret organization in various planets) that allows him just to follow their peregrinations during the search. I have to point out that he played just a session with us so his backstory have not been explored yet.
The problem I want to address is that due to our real life we have a really limited timeframe of playing time of 2 hours per week, and I feel this really constraining to the sanbox-style campaign I want to run.
I feel that these 2 hours of time are too little to "explore the sandbox" without diluting their plans and motivations during the campaign, in fact until now even avoiding random encounters and events not bound to their plans (and I agree with this answer) we advanced just a little in the campaign (speaking in campaign time, not real time).
Since it's a sandbox I'd like to add random encounters, side quests and so on, but I feel this will exponentially prolong the campaign at the point that the pacing of the events the PCs are taking part will slow to a crawl in real-life time.
What I'm asking
Have you suggestions on how to run a sandbox campaign with the limited playtime we have, with random encounters and events and side-quests?
Or should I drop my want-to-be sandbox style and go on with a plot-driven campaign (I mean, not railroading, but following and reacting to my players' actions and intentions without random events/encounters, side quests and so on)?
I know I should talk with my players and in fact I will. I'll ask them if they'd like random events and side-quests or if they prefer a more straightforward campaign without this sort of things. I'll also ask them If they care if this campaign will potentially go on "forever" and be slower in the resolution of things or if they'd like to see their motivations and plans end in a more limited time.
What I really care is to have more general approaches to this problems because I feel that I'll always (at least, as far as I can see in this part of my life) have this little timeframe to run my campaigns so I'll often have this problem. It's ok to have answers (or part of them) related to my actual problem with my actual campaign.
Thank you in advance!