In a Nutshell: Background
The Prophet (saw) started to meet his companions at Dar al-Arqam, the home of the companion al-Arqam, a few months after ba'thah (revelation). The Prophet (saw) was preparing the future activists and leaders of Islam here.
Dar al-Arqam was a house, far from the eyes of the Meccans, where the Prophet (saw) used to meet his companions, new converts and those seeking information about Islam.When did the Prophet (saw) enter Dar Al-Arqam?
The earlier books of seera are silent regarding this point, though some later latter books argued it took place before Umar (ra) embraced Islam by one or two months.
The tenth-century historian al-Halabi argued the companions used to secretly pray in the streets of Mecca. One day, a group of Meccan people noticed and fought them. Saad ibn Abi Waqas (ra) hit one of them with a camel bone and he died. This event took place in the fourth year of ba'thah as Mubarakpuri noted. (Mubarakpuri, ar-Rahiq al-Makhtum, p. 80)
Halabi argued the Prophet (saw) then hid with his companions (then around 39 companions he claims) in Dar al-Arqam for one month and it was then followed by the public dawa.
ِثُمَ دَخَلَ صَلَى اللّهُ عليهِ وسَلم وأَصْحَابُهُ مُسْتَخْفِينَ فِي دَارِ الأَرْقَمِ: أَي بَعدَ هَذِهِ الوَاقِعَة
"Then the Prophet (saw) and his companions (ra) secretly entered Dar al-Arqam; i.e. after this incident." (Halabi, as-Seera al-Halabiyya, Vol. 1, pp. 403)
Mubarakpuri also agreed with him and argued when the number of Muslims increased, the Prophet (saw) started to secretly meet them in Dar al-Arqam. (Mubarakpuri, ar-Rahiq al-Makhtum, the expanded edition, p. 456)
But this is improbable and based on no narrative evidence.
In addition, there are many early companions approaching the Prophet (saw)
enquiring about his call and they then converted in Dar al-Arqam. For example, Ammar and Suhayb (ra) converted very early in Islam there.
It was narrated Ammar (ra) met Suhayb ibn Sinan (ra) in front of the door of Dar al-Arqam. They then entered the house and asked the Prophet (saw) about Islam and subsequently converted to Islam.
Ammar (ra) narrated:
لَقِيتُ صُهَيّبًا عَلَى بَابِ دَارِ الأرْقَمِ وفِيهَا رَسُولُ اللهِ صَلى الله عليه وسلم ، فَدَخَلْنَا، فَعَرَضَ علَيّنا الإِسْلَامَ فَأَسْلَمْنَا
"I met Suhayb in front of the door of Dar al-Arqam and the Prophet (saw) was there. We entered and he presented Islam to us, so we embraced Islam." (Dhahabi, Siyar A'lam an-Nubalaa, Vol. 3, p. 350)
Ammar also narrated he was the ninth Muslim:
رَأَيْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم وَمَا مَعَهُ إِلاَّ خَمْسَةُ أَعْبُدٍ وَامْرَأَتَانِ وَأَبُو بَكْرٍ.
"I saw Allah's Messenger (saw) and there was none with him but five slaves, two women and Abu Bakr (i.e. those were the only converts to Islam then)." (Bukhari 3660, 3857)
So, Ammar (ra) converted very early in Islam, as the fifth-century muhaddith ibn Hubayrah Shaybani said:
فِي هَذَا الحَدِيثِ مَا يَدُلُ علَى قِدَمِ إسْلَامِ عَمَّار.
"This hadith proves Ammar became a Muslim early." (Ibn Hubayrah Shaybani, al-Ifsah 'An Ma'ani as-Sihah, Vol. 2, p. 137)
This suggests the Prophet (saw) entered Dar al-Arqam very early after a few months of ba'thah. There appears to have been a plan in the Prophet's (saw) mind early on for having a meeting place where he could meet with his followers. The same happened when he migrated to Medina, he created the masjid. The Role of Dar al-Arqam
As I said above, after extensive research I found there are no narrations that actually tell us what exactly the Prophet (saw) was doing there, but we could try to determine what happened by working backwards from the outcomes which are known through many evidences.
It was narrated the maximum number of companions in Dar al-Arqam was only forty men after the conversion of Umar and Hamzah (ra), whilst Muslims at that time doubled this number. (Salihi, Subul al-Irshad, Vol. 2, p. 319, Tabarani, al-Mu'jam al-Kabir 911, al-Hakim, al-Mustadrak 6130)
It is certainly true the Prophet (saw) selected some and was spiritually, intellectually, physically and religiously preparing these future leaders of Islam. (Abu Shuhbah, as-Seera an-Nabawiyyah, Vol. 1, p. 289)
For example, from Dar al-Arqam emerged the four Rightly Guided Caliphs (including Umar (ra) who stayed for a while before the collective public dawa).
It was the birthplace of the leading governors, messengers, military leaders, representatives and scholars of fiqh, Qur'an, hadith, tafseer and so on, such as ibn Mas'ud, Zayd ibn Haritha, Bilal, and others.
It was also narrated the Prophet (saw) used to appoint a teacher, for each new Muslim group, such as al-Khabab in the story of Umar's conversion. So, it seems the Prophet (saw) was preparing these forty men for leading roles.
It was also narrated the companions used to lead non-Meccans to inquire about Islam, such as Abu Dharr, ibn Adsah, and other converts arriving from outside Mecca to the Prophet (saw) in Dar al-Arqam.
So, the Prophet (saw) was certainly teaching them how to call to Islam and how to choose people who could influence the world. For example, Mus'ab would not be sent to Medina
with the group of al-Ansar without preparation for such an important role. Therefore, we find he followed a similar approach to, and probably acquired from, the Prophet (saw).
It seems like the Prophet (saw) was preparing them for two things: the collective dawa they later participated in and the leading of Muslim state when it is ready as the Prophet (saw) needs helpers to run it, people with a good understanding of Islam to manage people, society, call other societies, campaign etc. Conclusion
The Prophet (saw) started to meet his companions in Dar al-Arqam a few months after ba'thah. The Prophet (saw) was spiritually, intellectually, physically and religiously preparing the future leaders of Islam in Dar al-Arqam. References
Dhahabi, Siyar A'lam an-Nubalaa;
Halabi, as-Seera al-Halabiyya;
Ibn Hubayrah Shaybani, al-Ifsah 'An Ma'ani as-Sihah;
Salihi, Subul al-Irshad;
Mubarakpuri, ar-Rahiq al-Makhtum, the expanded edition;
Tabarani, al-Mu'jam al-Kabir;
Abu Shuhbah, as-Seera an-Nabawiyyah.