Air carrier Captain reported being assigned higher airspeed and altitude by ATC during an initial approach resulting in an unstabilized approach. The Captain took over the flight controls and performed a go around then returned for a landing.

Narrative

We were inbound for the ILS 22 in IMC. ATC kept us high and fast. We were at 4000 ft. doing 250kts passing YOMAN. I queried ATC about the altitude before we even got to YOMAN and they still wanted us at 4000 ft. I should have asked to slow down. ATC was very busy. Once they cleared us for the approach we were given 3000 ft. and to slow to 180 kts. The First Officer (FO) went full spoilers and 1500 ft. per minute on the vertical speed. I verbalized to the FO that it wasn't going to work. There was no way we were gonna be able to lose 2100 ft. and slow down in 5 miles. I switched to Approach on 134.9 and then over to Tower. At this point it was all happening fast since we were still too fast and descending too fast. I called that out again. The FO clicked off the Autopilot and were were in a 10 degree nose down pitch. ATC asked if we were gonna be too high as I'm taking over the flight controls to do the go around. ATC then gives us a low altitude alert. Between ATC giving us the low altitude alert; doing the go around in IMC; and the FO now having to take comms we blew through the 2000 ft. ATC gave us. We had 3000 ft. set for the missed approach altitude according to the approach plate and the fact that we were IMC on the ILS approach. As we were passing through 2000 ft. they gave us 3000 ft. and still runway heading. We completed the go around and came back to do the approach again. I kept the flight controls and did the approach and landing. When we came back around ATC did slow us this time but they kept us at 4000 ft. until turning in to the approach inside YOMAN again. I told the FO to ask for the descent and they said they would give it to us in a few seconds because they had departures at westchester (HPN) so I'm assuming that's why we were kept high initially.Cause: Airspeed too fast and altitude too high. I should have initially told ATC it wasn't going to work and to vector us back around. I also should have clearly stated to the FO to slow the descent rate and not worry about trying to save the approach. Suggestions: We should not be kept high and fast on the approach. I think we get so used to doing what ATC says in NY and making it work even when we know we're going to need something that they aren't able to do. Like a sooner descent; a turn in sooner because there's a tailwind and we'll blow through the localizer; or slow down to configure and we aren't able to request it because its so busy or even if we do they can't give it to us. I should have asked to slow down or just done it if we couldn't get a word in to ATC. If we would have been slower and already able to start configuring the aircraft then the altitude/descent wouldn't have been as much of a problem. Next time I will voice the concern right away to ATC instead of just confirming what they wanted us at so we could properly set up for the approach.