I would put the EULA with your installer. You can create an installer using something like NSIS: NSIS Quick Setup Script Generator - NSIS
There’s a lot you can do with that if you want to learn more about making installer scripts but it has a spot in there where you can select a Text file as your EULA so when they run the installer it will pop that up and agree to it to continue installing.
You don’t have to use the UE4 logo intro. That’s what the deal is with the Unreal trademarks, so if you want to use the logo anywhere you need to follow the branding guidelines and then get it approved.
I think you can put the disclaimer about using UE4 with the screen showing the Unreal logo or you could put it on the menu screen if you want.