Yes, that's possible using Automation for Jira. You just need to set it up to use a balanced workload.
If you're not familiar with Automation then the following link will take you to their community page: https://community.atlassian.com/t5/Automation-articles/Welcome-to-the-Jira-automation-community/ba-p/1388465
Their help guides are really useful, and this post in particular should help: https://blog.codebarrel.io/7-practical-automation-rules-to-turbocharge-your-jira-service-desk-62430d76d16d
If you scroll down to #3, they have a section on Auto Assigning
Hope that helps,
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