Update: I am mis-remembering slightly. This answer definitely applies to AD&D 1E DMG (I have now just seen a copy), but the same tables may not be available in the 2E DMG. If that is true I suspect groups I played in used it to help build higher level parties in 2E, effectively using the 1E DMG as a sourcebook for some of the extra tables. 1E and 2E AD&D are no more different than 3E and 3.5E D&D - a few rules and numbers changed, but enough remained the same that most material for 1E works without modification for 2E.
There is a listing of probabilities to have various starting magical gear in the DMG. It is quite conservative, and you need to be around 10th level before you are guaranteed some basic items.
Essentially the rule lists probabilities, by class, of having various types of magic item. Typically you roll D100 several times, looking to score less than some small multiplier of your level (e.g. a 7 x level % chance of a +1 weapon). Because you get a number of tries, it is normal to end up with one minor magic item as starting gear for a mid-level character. With 10k experience, your chances are probably quite low however, and it is likely some characters start with no magic items.
I no longer have the books. A quick search suggests that the rules I am remembering are in Appendix P of the DMG 1st Edition (I have not found them in 2nd Edition, but also not seen "proof" that it was only 1E).
So there are "official" rules for starting gear at higher level, but you shouldn't feel that you have to use them if you prefer to figure something else out. In fact, as they were published in 1E, and not available in 2E it is questionable whether they are considered official. However, early runs of D&D did not have quite the same emphasis on RAW 3E onwards, rulebooks were written with a lot of space for DM and player interpretation, and many rules were open-ended advice. That includes this Appendix P - it makes suggestions for how to start a higher level party, such as simply rolling a D3 to see what level you started at!