ERJ 170 Captain reported they were cleared by ATC to cross a runway with departing traffic but had to stop before crossing to avoid a possible collision.

Narrative

After landing and holding short of Runway XXL on Taxiway 1 we waited for several aircraft to take off. We were given a clearance to cross XXL on 1 and contact Ground. Before I started taxiing across the runway I looked and saw a 737 down around Taxiway 2 accelerating for takeoff. I had enough time to tell the FO we are waiting till the aircraft is clear before crossing and still watched him rotate and lift off just prior to Taxiway 1. It was a long enough delay that the FO did not read back the clearance fast enough that another airplane checked in and the Tower Controller hastily read back our clearance instruction. At that point the FO read it back and we crossed then taxied to the gate. Once at the gate I contacted Clearance Delivery for the Tower Supervisor phone number and called their recorded line to discuss the situation. They Supervisor picked up the phone got my information and had a Manager call me back.Suggestions: The supervisor manager who contacted me explained the controller used anticipation to clear us and according to the radar tape and recording tape they said the airplane was around Taxiway 3 when we were cleared. She did state the ASDEX does not indicate altitude on the radar tape until the airplane was at 100 feet and could not say if the airplane was airborne or not at our intersection. I described to the controller how much time I had to process what I saw and that had I not looked and waited I could have easily had the airplane across the hold short line and even onto the runway pavement. I don't think I could have been fully in the intersection but there was still a hazard of a collision had I been fast on the power application to taxi. The controller and I determined just reiterating to the working controller to pay attention to actual takeoff rates and performance; this was a 737 going to ZZZ1 so it's acceleration was slower than a normal 737. I also stated I would report this incident for trend monitoring in case this becomes an issue at ZZZ.