Modpack version
1.76a

Issue
Game crashes at startup after some time of loading. If I don't use the bundled java, then the game will crash immediately and won't show a crash report

Logs
https://pastebin.com/UHsiAcWG

You are indeed crashing due to the outdated Java.
If you crash while using your system Java, then it's either 32-bit or newer than Java 8.

You can find Java 8, 64-bit here: https://www.java.com/en/download/manual.jsp, by choosing the Offline Installer

Java Downloads for All Operating Systems

Java manual download page. Get the latest version of the Java Runtime Environment (JRE) for Windows, Mac, Solaris, and Linux.