1A relay replace by IGBT
It is technically possible, but you will have very high losses to deal with. 

At 500A the voltage drop is around 2V according to the datasheet. So the IGBT will continuously produce 1KW. The thermal resistance \$R_{th,JC} = 0.12 K/W\$ means that the junction temperature will be 140°C (already too hot for reliable long-term operation), even if you somehow keep the IGBT case at 20°C (ideal cold plate emlpoying e.g. two-phase cooling or heat pipes). 

With the selected IGBT you can only employ one of the two inside the package, so this is not perfect as well. Furthermore, the 650V maximum voltage is quite close to your operating voltage, maybe you might look for a higher voltage class (although the losses will be higher, too). 

Paralleling IGBTs would help a little bit in terms of losses and allow better cooling,  but would also increase cost significantly. E.g. two such IGBTs in parallel will have a voltage drop of around 1.3V, resulting in total losses of 0.65kW during operation (325W per IGBT) which you could cool with a heat sink of size around \$V_{HeatsinkPlusFan} = 5 dm^3\$ employing forced convection.