With historical records alone, it is impossible to ascertain the exact date when Gojoseon was founded. We do know that Joseon existed by at least the 4th century BC; in the Records of the Grand Historian, a figure from the Yan State who lived in the 4th century BC mentions "Joseon" as an eastern neighbor of the Yan State. Later, it is noted in both Records and another book titled Weie (魏略) that Joseon lost its western lands to the Yan State. The Weie goes into more detail; it says that Joseon lost 2000 li of its western territory to Yan during the early 4th or late 3rd century BC (archaeological evidence indicates that Gojoseon retreated south of the Chongchon River around this time, seemingly abandoning its territories in Liaoning). Obvioudly, 2000 li is an exaggeration, because if this was true this would mean that Joseon extended to Yanjing, which is ridiculous, but this does indicate Gojoseon control over Liaoning, which is also supported by archaeological evidence.

The "Haineibei jing" chapter of the Shan Hai Jing mentions Joseon:

朝鮮在列陽東 海北山南 列陽屬燕

Which translates roughly to

Joseon is to the east of Lieyang, and to the south of Beihaishan Mountain. Lieyang belongs to the Yan State.

However, the Shan Hai Jing was written by many people at different times, and the Yan State existed for centuries, so this record does not really ascertain the time of Gojoseon's founding. All we learn is that Gojoseon existed prior to the Qin unification, which we already knew from other texts.

The Guanzi also mentions an entity called Baljoseon (Fachaoxian) trading with the Qi State of the Shandong Peninsula. However, the Guanzi is believed to have been written mostly during the Warring States Period, so all we learn is that there was something the Chinese referred to as Chaoxian during the Warring States Period, which we already knew.

So all we can learn from written evidence is that Gojoseon had power over Liaoning in the 4th century BC. So to ascertain the rough founding dates of Gojoseon we must rely on archaeology.

Early Gojoseon sites generally include characteristic guitar-shaped bronze swords and by dolmen tombs. Consensus is that these date from the 10th century BC, so the foundation of Gojoseon as a cultural entity probably occurred around that time.

The extinct state of Joseon/Chaoxian doesn't fit the modern day narrative of being a "Korean" nation or belonging to "Korean" ethnicity as Chinese texts show that the entity or geographic location known as Chaoxian started out in Northeastern China.

Tangun has no historic basis and is a result of nation building similar to Shennong being revered by the Vietnamese.

While Jizi most likely existed as a historical figure whether or not he has anything to do with the Marquis Ji(㠱侯) mentioned in the bronze vessels excavated modern day Liaoning is still up to debate. http://i.imgur.com/URv6Djk.jpg

Efforts to pinpoint identity are hindered by the lack of primary sources dating towards Joseon/Chaoxian entities.

Pre Han texts include the Guanzi,Zhan Guo Ce,Shan Hai Jing etc which do not associate Jizi with Chaoxian.

Guanzi 陰山之礝碈，一筴也。燕之紫山白金，一筴也。發朝鮮之文皮，一筴也。汝、漢水之右衢黃金，一筴也。江陽之珠，一筴也。秦明山之曾青，一筴也。禺氏邊山之玉，一筴也。 Precious gemstones of Mt.Yin,silver of Mt. Zi of Yan,exotic colored animal hides of the Fa Chaoxian,gold from the Ru and Han rivers,pearls of Jiangyang,azurite from Mt. Qinming and jade from Mt. Bian of the Yu clan. http://ctext.org/guanzi/kui-du

Here Master Guan is explaining the 7 treasures of the world to Duke Huan of Qi.

Zhan Guo Ce 燕東有朝鮮、遼東，北有林胡、樓煩，西有云中、九原，南有呼沱、易水。 To the east of Yan lies Chaoxian,Liaodong,to the north Linhu,Loufan,to the west Yunzhong,Jiuyuan and to the south Hutuo,Yishui. http://ctext.org/zhan-guo-ce/su-qin-jiang-wei-cong-bei

Chaoxian is assumed to be west of Liaodong due to the fact that when Su Qin is taken into account Jiuyan is farther away than Yunzhong while Yishui is farther away than Hutuo.

Shan Hai Jing 朝鮮在列陽東，海北山南。列陽屬燕。 Chaoxian lies to the east of Lie river,north of the sea and south of the mountain,which is ruled by Yan. http://ctext.org/shan-hai-jing/hai-nei-bei-jing

東海之內，北海之隅，有國名曰朝鮮。 Within in the Eastern Sea,and just touching the Northern Sea lies the state of Chaoxian. http://ctext.org/shan-hai-jing/hai-nei-jing

The Lieyang used here most likely refers to the Lie river which Han era sources such as Fangyan note about Chaoxian. The Northern sea here is none other than the Bo Sea,the Eastern Sea is the Yellow Sea,while the Taihang mountain range has been identified as the mountain in this quote.