Balrog and servants of Sauron

[the phantom]

'Sauron begins to people Moria with his creatures' in the year 2480 of the Third Age

Yes, it is definitely useful to mention that the year was 2480 because that is important to samrohan's questions.

In 2480 Sauron was at Dol Guldur, not Mordor, so if he was literally sending forces (from right where he was) to Moria then his creatures certainly did not have to pass through Rohan or Gondor (since they would already be well to the north of them).

The entire entry for 2480 (actually, for c. 2480) reads-

Orcs begin to make secret strongholds in the Misty Mountains so as to bar all the passes into Eriador. Sauron begins to people Moria with his creatures.

It's not clear to me where exactly the orcs are coming from. All we know is that Sauron wanted them in Moria. He could've sent them from his base of operations or simply sent orders to orcs in the mountains further north to move down to Moria.

And also, the orcs we see in Lord of the Rings might not have much of a connection with the Orcs that were ordered to populate Moria around 2480. A vast majority of the orcs in the Misty Mountains were wiped out of existence during the War of the Dwarves and the Orcs (which began in 2793).

From App A-

they assailed and sacked one by one all the strongholds of the Orcs that they could find from Gundabad to the Gladden...they hunted for Azog in every den under mountain...all the orcs that fled before them were gathered in Moria

Considering that the orcs gathered in Moria, that the final battle was fought outside the doors of Moria, and that the dwarves won the day, I can't imagine that very many orcs were left in Moria after that.

And since there is no other mention (that I can remember) of Sauron sending masses of orcs to Moria we can probably assume that the "legions" that were in Moria when the Fellowship passed through were simply a result of orcs migrating there from other parts of the Misty Mountains and that the orcs were likely reproducing fairly quickly.