I agree, unfortunately you have to upgrade almost all of your parts. Haswell or Skylake 4-core with SSD and 16GB of RAM. GTX 970 4GB or 980Ti 6GB.
If your budget is $2,000 you should be able to squeeze a GTX 960 4GB into it and then upgrade that later (SLI is not really useful at this point for UE4).
In fact, Nvidia’s Pascal is out next year so by end of 2016 there should be some amazing GTX 1000 series cards (if they are named as such). It may not be worth getting a 970 or 980Ti right now unless you know you’re going to max it out.