Putting the context given away, the sentence can be correct for every native German speaker.

Example: Think of a recurring event that used to start at around 3 PM. Then the organizer decided that 3 PM is not a good time and moved it to, say, 5 PM. And now, eventually, they moved it again to an even later time — 8 PM that is.
Then the sentence "Jetzt ist es schon um 8 Uhr."¹, most likely said in a frustrated voice, is perfectly valid. Note that jetzt doesn't refer to at this moment but to at the present time. And um clearly indicates that it is not necessarily an exact time.

Your given context, however, is a little weird. You refer to the time right now. You would give either the precise time (it's 3 minutes to 8), or an approximate time either without any indication that it isn't exact (it's 8) or with a hint that it's not too precise (it's shortly before 8).

While um certainly fits the third case, it's not common at all. It might be that a few German (or Austrian or Swiss, for that matter) use it colloquially, but I don't know nothing about that.

So, if the context is that that current time is being asked, don't use um.

¹ In the scenario I described above, erst would be more likely to be used over schon. Luckily, that doesn't weaken my argument at all. Actually, you would possibly even say "Jetzt ist es schon erst um 8 Uhr.", but that's not of matter in respect to the question.

Putting the context given away, the sentence can be correct for every native German speaker.

Example: Think of a recurring event that used to start at around 3 PM. Then the organizer decided that 3 PM is not a good time and moved it to, say, 5 PM. And now, eventually, they moved it again to an even later time — 8 PM that is.
Then the sentence "Jetzt ist es schon um 8 Uhr."¹, most likely said in a frustrated voice, is perfectly valid. Note that jetzt doesn't refer to at this moment but to at the present time. And um clearly indicates that it is not necessarily an exact time.

Your given context, however, is a little weird. You refer to the time right now. You would give either the precise time (it's 3 minutes to 8), or an approximate time either without any indication that it isn't exact (it's 8) or with a hint that it's not too precise (it's shortly before 8).

While um certainly fits the third case (usually with a definite article), it's not common at all, except you don't know the exact time. It might be that some German (or Austrian or Swiss, for that matter) use it colloquially more frequently even if they know the exact time, but I don't know nothing about that.

So, if the context is that that current time is being asked, don't use um.

¹ In the scenario I described above, erst would be more likely to be used over schon. Luckily, that doesn't weaken my argument at all. Actually, you would possibly even say "Jetzt ist es schon erst um 8 Uhr.", but that's not of matter in respect to the question.

Putting the context given away, the sentence can be correct for every native German speaker.

Example: Think of a recurring event that used to start at around 3 PM. Then the organizer decided that 3 PM is not a good time and moved it to, say, 5 PM. And now, eventually, they moved it again to an even later time — 8 PM that is.
Then the sentence "Jetzt ist es schon um 8 Uhr."¹, most likely said in a frustrated voice, is perfectly valid. Note that jetzt doesn't refer to at this moment but to at the present time. And um clearly indicates that it is not an exact time.

Your given context, however, is a little weird. You refer to the time right now. You would give either the precise time (it's 3 minutes to 8), or an approximate time either without any indication that it isn't exact (it's 8) or with a hint that it's not too precise (it's shortly before 8).

While um certainly fits the third case, it's not common at all. It might be that a few German (or Austrian or Swiss, for that matter) use it colloquially, but I don't know nothing about that.

So, if the context is that that current time is being asked, don't use um.

¹ In the scenario I described above, erst would be more likely to be used over schon. Luckily, that doesn't weaken my argument at all. Actually, you would possibly even say "Jetzt ist es schon erst um 8 Uhr.", but that's not of matter in respect to the question.

Putting the context given away, the sentence can be correct for every native German speaker.

Example: Think of a recurring event that used to start at around 3 PM. Then the organizer decided that 3 PM is not a good time and moved it to, say, 5 PM. And now, eventually, they moved it again to an even later time — 8 PM that is.
Then the sentence "Jetzt ist es schon um 8 Uhr."¹, most likely said in a frustrated voice, is perfectly valid. Note that jetzt doesn't refer to at this moment but to at the present time. And um clearly indicates that it is not necessarily an exact time.

Your given context, however, is a little weird. You refer to the time right now. You would give either the precise time (it's 3 minutes to 8), or an approximate time either without any indication that it isn't exact (it's 8) or with a hint that it's not too precise (it's shortly before 8).

While um certainly fits the third case, it's not common at all. It might be that a few German (or Austrian or Swiss, for that matter) use it colloquially, but I don't know nothing about that.

So, if the context is that that current time is being asked, don't use um.

¹ In the scenario I described above, erst would be more likely to be used over schon. Luckily, that doesn't weaken my argument at all. Actually, you would possibly even say "Jetzt ist es schon erst um 8 Uhr.", but that's not of matter in respect to the question.