Vayeitzei 28:11. Vayikach mei’avnei hamakom. The Headrest and the Altar.

In the morning, Yaakov took the stone and made it into a Matzeivah. Why did he wait till morning to make the Matzeivah?
Netziv– better to daven during the day.
R’ Meir Simcha– the avodah of korbanos has to be in during the day.
Brisker Rov brought in Shai LaTorah– making the mizbei’ach was like hakrovoh, which must be during the day.
Ragotchover in Shai LaTorah– "beyom hakim es hamishkan,"only may build the Mishkan during the day, (from Shvu’os 15b and Rambam BHB 1:12), and this had a din Mishkon.

There is a question as to what Yaakov was doing, only binyan (Rogotchover) or also hakravah Rav Meir Simcha), or perhaps putting up a matzeivah at that time was avodah mamash, not merely a preparation for avodah (Gri’z).

Throughout sefer Breishis we find the Avos putting up Matzeivos without any mention of hakravah, just "vayikra b’sheim Hashem." In fact, there is a machlokes rishonim about the function of these matzeivos. Harav David Oppenheimer pointed out the Ibn Ezra that says that the Matzeivoh was not a bomoh or a mizbei’ach, it was just a structure erected to honor Hashem, and the oil poured on them was not a korbon. This makes sense, because if they were only places for a hakrovoh, it could have said "and he was makriv korbonos to Hashem" without talking about the matzeivoh he built. This indicates that the main point was the building of the Matzeivoh.

If, in fact, these things were not bamos, I think that they are unique in all of the Torah– because I can’t think of any other place that we serve Hashem by erecting a structure. The Mishkon was built to enable the avodas Korbanos, it was not tachleisi (a purpose in itself).

The Ramban in R’ei, Dvorim 16:22, where it talks about how Hashem hates Matzeivos, says they are monuments where people gathered. See B’reishis Raba 81:2, Vayikra Raba 37:1, Tanchuma Vayishlach 8, Zohar Bereishis 175a, see also Rashi Bereishis 35:1.

Also, R Meir Simcha in 35:8 says that Yakov first made a Neder (B’reishis 28:22, see Rashi there), that he would return to offer Nesochim to Hashem once again on the same Matzeivah that he set up now, on his way to Lavan. When he finally returned, though, Hashem told him to erect a new Mizbei'ach and not to use the Matzeivah as he had promised (B’reishis 35:1,7). Why the change? He says that in the interim, they were co-opted by ovdei Avodoh Zoroh and they became sonui, so Yaakov couldn’t use his old Matzeivoh.)

Back to the original question: as soon as Yaakov saw the holiness of the place, why didn’t he immediately do avodah there. My teretz– Rashi says Hashem folded and put all of Eretz Yisroel under him as he slept. So he couldn’t build and use the matzeivah until it was exclusively in the chelek of Binyamin. Only after the land of the other shvatim went home and it was left in its natural state which was Binyamin’s land could he build the matzeivah.

Now, we know that the reason Binyamin was zocheh to have the mizbei’ach in his cheilek was because he didn’t bow to Eisov, and the story here was before they met Eisav. But this doesn’t matter, because l’maiseh it has to be in chelko shel Binyamin, and maisei Avos simon l’banim, so it had to be there then too. The honest truth is that this is a silly question; it is wrong to think the story with Eisav was the reason Binyamin was zocheh to have the mizbei’ach in his cheilek. It could be that the mizbei’ach had to be in that particular spot because of the unique k’dushas hamakom. The story with Eisov was not the reason the Mizbei'ach was built in Binyamin's territory, it was the reason Binyamin was given the territory that the mizbei’ach had to be built in.