Pardon intrusion ... but ... it's been my experience that there is a reason for a site to wait so long to upgrade moodle. Is there? We may not be getting the full story ... just the question.
See by an earlier posting the operating system is RedHat ... but whet version of RedHat - truely RedHat with 'entitlements' up to date? Important as along your march of the moodle will come upgrades to PHP and DB (MySQL or MariaDB). RedHat has been traditionally conservative when it comes to providing PHP versions as well as DB (MySQL/MariaDB) versions. Which means one will have to resort the trusted 3 party repos - like Remi - to acquire needed upgraded to PHP.
How many additional plugins to the Moodle are there? And do those plugins have a compatible version for destination version of Moodle? Theme's are plugins. And, other than language, has core code been altered in any way?
The safest route is to clone the instance and 'practice' the march upwards to see what catch 22's and gotcha's might raise their ugly heads.
If that is not possible, moving forward using caution at each hop upwards.
What you could do now that would be of benefit for you and for sharing info .... login as admin level, go to Server, Environment - update component. Then use the drop down pick list of moodle versions and set that to 3.5 the nearest LTS version to your 3.3.x. Note what things in red and or yellow. What are they?
Red's mean they have to be addressed *before* attempting upgrade to that version. Yellows can become Reds the higher up one goes.
As you can tell, me thinks it's a deeper iceburg here! (I might be wrong!)
'SoS', Ken