In C:M 259:1 the Aruch haShulchan says it starts once you see the object. However, there are conditions to be met.
For example: In C"M 263:2 he says that mitzvas asei of hashavas aveidah applies even to a dignified personality once he picks it up or moves it. Otherwise, Mr. VIP is exempt.
In CM 263.2 the topic treated is the lav "לא תוכל להתעלם". This lav has exceptions when there is a problem of honor. "פעמים שאתה מתעלם, זקו ואינו לפי כבודו". The sugia is in BM 30ab. The same reason that leads us to say "אתה מתעלם" leads us to push out the asse of "השב תשיבם"
If you have already picked up the object, there is still Mitsva "השב תשיבם" despite it was pushed out. Now, you must report it to the owner. This mitsva still exists but was pushed out. If you make the choice to make it by beginning to return the object to its owner you are now in duty to make it. This is the meaning of the text in Aruch Hashulchan.
The Gemara explains that it is possible to apply the "פעמים שאתה מתעלם", for the same reason the positive mitsva of "השב תשיב" is pushed out. But when he begins to take the object, he decides to make the mitsva of "השב תשיבם". In conclusion, when there is no "לא תוכל להתעלם", there is no obligation to make "השב תשיבם" despite that the mitsva exists. But if, regardless of any obligation he takes it, the Mitsva of "השב תשיבם" comes back. The explanations of the pushing out of this misva are multiple. The main is that a mitsva regarding money laws doesn't push out Isurim. So, Isurim push it out.
The general rule of "השב תשיבם" is explained in 259.1. The two mitsvot are here when he identies the Aveda. That is the line of the Ran from which the Nimuke Yosef is quoted, and the Rambam. The Taz and Aruch Hashulchan follow them. Other poskim as the Sma follow the Ramban who holds that "השב תשיבם" begins from the time he takes the object.
In 259.1 The Aruch Hashulchan says following the Taz quoting the Nimuke Yosef for the Pshat on Gemara 26b.
המתין לה עד שנתיאשו הבעלים ונטלה אינו עובר אלא משום לא תוכל להתעלם בלבד
THe pshat is that because he stands guard next to the object he has still the possibility to make the Mitsva of "השב תשיבם" he doesn't annul it. But when the Yeush occurs, the Mitsva disappears. But if he goes away and doesn't stands guard next to the object, he annul both "השב תשיבם ולא תוכל להתעלם". The proof is from the Gemara 30a quoted below with Rashi.
האי עשה - השב תשיבם
He has a positive Mitsva, Hashev Teshivem. And the question is when he doesn't take the object.
for a man who has no obligation of "לא תוכל להתעלם" in a precise case, there is a positive mitsva of "השב תשיבם"but it is pushed out, pushed out.
In a special situation that regardless the lack of "לא תוכל להתעלם" and the pushing out of the asse, he takes the object, he makes the choice to make the asse despite the dechia. The asse comes back.
For a man who has an obligation of "לא תוכל להתעלם", there is immediately a Mitsva of "השב תשיבם".