Is the date quickset?
If it is maybe the day of the week is not QS and the watch must be stopped and restarted on the correct day. I have a few vintage day and date watches made this way, not any of them being Universal Geneve though.
Something else...does it have more than one language on the day disc? You may need to see the day changing to tell but I have no idea how to adjust it to the desired language if it has two.
Note: It is not a good idea to run the hands around and around to set the day or date because it can result in wear to the 'canon pinion' which is basically a slip clutch so time can be set without damage to the watch works.
If you could find out what caliber (calibre) the movement is, you should be able to find information about it on the internet. To find the caliber number you will need to find a similar watch on the internet and see if the movement specs are listed. A similar watch may not need to be solid gold, it can be 'gold cap/gold top' or stainless steel.
'Gold cap/gold top' = a layer of gold is pressed and soldered onto the case top.
Do not let just anyone open the watch up to see what caliber it has if you can not find the info on the internet because 18K gold is soft and prone to damage.
In my experience, many so called 'watchmakers' cause as much damage to watches as the owners/careless owners.
Btw...I had a similar nos 'gold top' Universal Geneve in 1996 but it was quickly sold without looking in it and I can not remember if it was quick set or not. I have the serial number but not the caliber, probably number 72.
Collectors Note: Matching Polerouter dials with movement calibers | The Polerouter Reference Website (universalgenevepolerouter.com)