When did Krishna and Arjuna meet for the first time?

Question

I want to know when Shree Krishna and Arjuna met for the first time. (if the answer is in childhood, please mention when they first met as youth too.)

Answer 1

They met for the first time after Draupadi's Swayamvara. In this chapter of the Adi Parva of the Mahabharata, Krishna and Balarama see the Pandavas for the first time during Draupadi's Swayamvara:

And beholding those feats of both Jishnu and his brother, Damodara (Krishna) of superhuman intelligence and inconceivable feats, addressing his brother, Halayudha (Valadeva) of fierce energy, said, 'That hero there, of tread like that of a mighty lion, who draweth the large bow in his hand four full cubits in length, is Arjuna! There is no doubt, O Sankarshana, about this, if I am Vasudeva. That other hero who having speedily torn up the tree hath suddenly become ready to drive off the monarchs is Vrikodara! For no one in the world, except Vrikodara, could today perform such a feat in the field of battle. And that other youth of eyes like unto lotus-petals, of full four cubits height, of gait like that of a mighty lion, and humble withal, of fair complexion and prominent and shining nose, who had, a little before, left the amphitheatre, is Dharma's son (Yudhishthira). The two other youths, like unto Kartikeya, are, I suspect, the sons of the twin Aswins. I heard that the sons of Pandu along with their mother Pritha had all escaped from the conflagration of the house of lac.' Then Halayudha of complexion like unto that of clouds uncharged with rain, addressing his younger brother (Krishna), said with great satisfaction, 'O, I am happy to hear, as I do from sheer good fortune, that our father's sister Pritha with the foremost of the Kaurava princes have all escaped (from death)!

Immediately after the Swayamvara, Krishna introduces himself to the Pandavas, as described in another chapter of the Adi Parva of the Mahabharata:

The sons of Pandu, then, hearing those words of their eldest brother, began to revolve them in their minds in great cheerfulness. The hero of the Vrishni race (Krishna suspecting the five persons he had seen at the Swayamvara to be none else than the heroes of the Kuru race), came accompanied by the son of Rohini (Valadeva), to the house of the potter where those foremost of men had taken up their quarters. On arriving there, Krishna and Valadeva beheld seated in that potter's house Ajatasanu (Yudhishthira) of well developed and long arms, and his younger brothers passing the splendour of fire sitting around him. Then Vasudeva approaching that foremost of virtuous men--the son of Kunti--and touching the feet of that prince of the Ajamida race, said, 'I am Krishna.' And the son of Rohini (Valadeva) also approaching Yudhishthira, did the same. And the Pandavas, beholding Krishna and Valadeva, began to express great delight. And, O thou foremost of the Bharata race, those heroes of the Yadu race thereafter touched also the feet of Kunti, their father's sister.

As you can see from the timeline here, this was when Krishna and Arjuna were 37 years old, or 52 years before the Mahabharata war.

Answer 2

AFAIK Lord Krishna and Arjuna met first after Draupadi's Marriage. Lord Krishna has identified Pandavas in Draupadi's Swayamvara but did not met (as written in Mahabharata, Adi Parva, SECTION CLXLI).

And beholding those feats of both Jishnu and his brother, Damodara (Krishna) of superhuman intelligence and inconceivable feats, addressing his brother, Halayudha (Valadeva) of fierce energy, said, 'That hero there, of tread like that of a mighty lion, who draweth the large bow in his hand four full cubits in length, is Arjuna! There is no doubt, O Sankarshana, about this, if I am Vasudeva. That other hero who having speedily torn up the tree hath suddenly become ready to drive off the monarchs is Vrikodara! For no one in the world, except Vrikodara, could today perform such a feat in the field of battle. And that other youth of eyes like unto lotus-petals, of full four cubits height, of gait like that of a mighty lion, and humble withal, of fair complexion and prominent and shining nose, who had, a little before, left the amphitheatre, is Dharma's son (Yudhishthira). The two other youths, like unto Kartikeya, are, I suspect, the sons of the twin Aswins. I heard that the sons of Pandu along with their mother Pritha had all escaped from the conflagration of the house of lac.'

After that Krishna and Balarama followed Pandavas and met them to the Potter's house where Pandavas were leaving those days (as mentioned in Mahabharata, Adi Parva, SECTION CLXLIII).

The hero of the Vrishni race (Krishna suspecting the five persons he had seen at the Swayamvara to be none else than the heroes of the Kuru race), came accompanied by the son of Rohini (Valadeva), to the house of the potter where those foremost of men had taken up their quarters. On arriving there, Krishna and Valadeva beheld seated in that potter's house Ajatasanu (Yudhishthira) of well developed and long arms, and his younger brothers passing the splendour of fire sitting around him. Then Vasudeva approaching that foremost of virtuous men--the son of Kunti--and touching the feet of that prince of the Ajamida race, said, 'I am Krishna.' And the son of Rohini (Valadeva) also approaching Yudhishthira, did the same. And the Pandavas, beholding Krishna and Valadeva, began to express great delight. And, O thou foremost of the Bharata race, those heroes of the Yadu race thereafter touched also the feet of Kunti, their father's sister. And Ajatasatru, that foremost of the Kuru race, beholding Krishna, enquired after his well-being and asked, 'How, O Vasudeva, hast thou been able to trace us, as we are living in disguise?' And Vasudeva, smilingly answered, 'O king, fire, even if it is covered, can be known. Who else among men than the Pandavas could exhibit such might? Ye resisters of all foes, ye sons of Pandu, by sheer good fortune have ye escaped from that fierce fire. And it is by sheer good fortune alone that the wicked son of Dhritarashtra and his counsellors have not succeeded in accomplishing their wishes. Blest be ye! And grow ye in prosperity like a fire in a cave gradually growing and spreading itself all around. And lest any of the monarchs recognise ye, let us return to our tent.' Then, obtaining Yudhishthira's leave, Krishna of prosperity knowing no decrease, accompanied by Valadeva, hastily went away from the potter's abode.'"