I would like to post an answer contrary to the general trend of the other by motivating it. Downvoters, please try to be in the OP's shoes for a very second.
I am going to say be careful and consider skipping it this time.
Look from the manager's point of view. This episode happened once, from your question it seems that you have requested, and was then approved, to enter the office earlier to complete some tasks. Unfortunately your computer thought it was non-duty hours and planned an update. There are ways in Windows to skip an update once or for a while, but you haven't used them. Likely, you didn't foresee that the update was taking a lot of time.
If you come on time and your computer takes 30 minutes to boot up, preventing you from doing your job, you can still blame the IT for not having configured proper policy updates (one of my customers schedules boot up and check-for-update of every workstation at night time).
But here you have requested for an exception to come earlier, your manager granted you to have the opportunity to work more and being paid more and... you lost your chance?!?!!
If I was your manager, I would have started questioning myself about giving you this opportunity again.
Here is my advice, since you did not say how earlier did you come to work:
- If you lost only 30 minutes over more hours, I would consider giving away just this half an hour for once in your life. For example bill 1,5 hours instead of 2
- If you came exactly 30 minutes earlier, I see no need in the whole question. You could apologize with your boss sorry, my computer was updating and act like you had clocked in on time
- You could also do some extra half an hour at the end of your shift, once
The key to my answer is that if it's a single episode you can consider giving some of your time to your company for a problem that was not your fault but your responsibility. Looking responsible about your acts can be helpful in your future career, e.g. during periodic reviews.
Of course there are two boundaries that must not be crossed:
- Make sure giving time away doesn't happen again, or worse often, because it will turn against you, and bad. If you start giving free hours for updates and similar IT tasks the company will be tempted to deduct as many hours as they like with trivial excuses, including coffee and bathroom breaks. This may even be illegal
- Acting responsibly never means that you are guilt for your responsibilities and have to pay damage for faults. You look like a salaried employee, so you are exempt from business risks. The risks are 100% up to the enterpreneur running your company, and cannot fall to the invididual employees' heads
Bottom line: your time is valuable and company must respect you as a professional, but still, we are talking about half an hour happened only once.