Not according to this wiki (if you click on the link, the articles provide citations from the prologue “Concerning Hobbits” in The Lord of the Rings):
Harfoots were the most common type of hobbit, and in their earliest known history they lived in the lower foothills of the Misty Mountains, in the Vales of Anduin, in an area roughly bounded by the Gladden River in the south and the small forested region where later was the Eagles Eyrie near the High Pass to the north.
The Harfoots were the first to migrate westward into Arnor, and there the Dúnedain named them Periannath or halflings, as recorded in Arnorian records around TA 1050. They tended to settle down for long times, and founded numerous villages as far as Weathertop.
By the 1300s of the Third Age, they had reached Bree, which was the westernmost home of any hobbits for a long while.
The Harfoots were joined between TA 1150 and TA 1300 by the Fallohides and some Stoors. The Harfoots took Fallohides, a bolder breed, as their leaders. The Shire was colonized long after this, in TA 1601, mostly by Harfoots.
Re: https://lotr.fandom.com/wiki/Harfoots
The Hobbits first begin migrating to Eriador beginning with the Harfoots
Re: https://lotr.fandom.com/wiki/TA_1050
It is unknown when Hobbits first appeared in Arda. They are only known to have originated somewhere in the valley of the Anduin River. By the time they were discovered by the other peoples of Middle-earth, they had already been around for many generations. The earliest known group of hobbits lived in the Vales of Anduin, in the region of Wilderland between Mirkwood and the Misty Mountains. According to The Lord of the Rings , they forgot any genealogical ties to the “Big People” (Men). At this time, there were three breeds, or tribes, of Hobbits, with different physical characteristics and temperaments: Harfoots, Stoors and Fallohides. While situated in the valley of the Anduin River, the Hobbits lived close by the Éothéod , the ancestors of the Rohirrim, and this led to some contact between the two. As a result, many old words and names in Hobbitish are derivatives of words in Rohirric.
About the year TA 1050, they undertook the arduous task of crossing the Misty Mountains. Reasons for this trek are unknown, but it possibly had to do with Sauron’s growing power in nearby Greenwood, which was later named Mirkwood because of the shadow that fell on it. The Hobbits took different routes in their journey westward, but as they began to settle together in Bree-land, Dunland Angle formed by the rivers Hoarwell and Loudwater; the divisions between the Hobbit-kinds began to blur. In the following centuries some of the Stoors, dismayed by the power of Angmar and a change in the climate of Eriador, fled east over the Misty Mountains. This group of refugees eventually gave birth to Sméagol, but their fate is ultimately unknown, as their dwellings were abandoned by the end of the Third Age, likely as the Misty Mountains had become infested by Orcs.
Re: https://lotr.fandom.com/wiki/Hobbits
So they were introduced as three strains of Hobbits of varying appearances (much like humans had become different strains over time many millennium ago) and then reunited (much like humans have in various places, most notable, the USA) in the Third Age.