Change your stats to include min(_time) or earliest(_time) . The latter is faster, but the former is going to be correct if you indexed things out of chronological order.
For example,
sourcetype=priorityEvents
| rex field=_raw "User\sID\s(?<user_id>.\d{0,8}+)"
| stats count as count, earliest(_time) as date_firstoccurance by user_id
| where count > 1
Note, if your timestamps are not in the date format you want, then you will need to add another eval to get the field date_firstoccurance in the correct format.
| eval date_firstoccurance = strftime(earliest, "%m/%d/%Y")
So your full query might be
sourcetype=priorityEvents
| rex field=_raw "User\sID\s(?<user_id>.\d{0,8}+)"
| stats count as count, earliest(_time) as earliest by user_id
| where count > 1
| eval date_firstoccurance = strftime(earliest, "%m/%d/%Y")
| table date_firstoccurance user_id count
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