My two cents is to wire the heated bed directly to your +12V supply without the SSR for a test. If it still struggles to get above 45C with no SSR in line, then the SSR isn't the cause of your problem.
I can tell you that my 300mm diameter Onyx heatbed (delta printer) took 40 minutes to reach 95C when run from 12V, and struggled to reach/hold 100C when I was trying to hit 110C. I picked up a Mean Well SP-600-24 (600 watt, 24V) power supply a few weeks ago, turned the output trimpot down to 19.5V, and now my warmup time is 6 minutes to 110C with no problem maintaining that temperature.....
I can tell you that my 300mm diameter Onyx heatbed (delta printer) took 40 minutes to reach 95C when run from 12V, and struggled to reach/hold 100C when I was trying to hit 110C. I picked up a Mean Well SP-600-24 (600 watt, 24V) power supply a few weeks ago, turned the output trimpot down to 19.5V, and now my warmup time is 6 minutes to 110C with no problem maintaining that temperature.....