because the entire race being wiped out was an exaggeration.
first off we know at the start of the series there were some Quincy still around such as as Uryu was being trained by his grand father Soken while Uryu's father was "retired" from being a Quincy so it's clear that they hadn't been all wiped out, more so we later learn that
Ichigo's mother Masaki is a Quincy
so the survivors from when they were "wiped out" was not limited to a single family
in the 1000 Year Blood War Arc we find out that hundreds of years before the Quincy was wiped out there was another conflict between the Quincy and the Soul Reapers in which the Quincy Progenitor, Yhwach, lost his powers after this battle and didn't resurrect for 990 years (900 years for his body to revive and 90 years to regain intellect) +9 more years for him regaining his former powers.
About 1,000 years ago, under unknown circumstances, Genryūsai Shigekuni Yamamoto failed to kill him. Sometime around or during the course of this event, Yhwach witnessed the capabilities of Yamamoto's Bankai, Zanka no Tachi. After his battle with Yamamoto, Yhwach supposedly lost his powers. Quincy folklore spoke of him as "The Sealed King": after 900 years of being sealed, he would regain his pulse; after another 90, he would regain his intellect; and after 9 more years, he would absorb the power of every "impure" Quincy to make their abilities his own.
Source: Yhwach > History (4th Paragraph)
after Yhwach's defeat the remainder of the Quincy who followed him went into hiding in the Seireitei and used the Reishi to create a invisible space where they hid waiting for Yhwach's return, these Quincy were called the Wandenreich.
Since the Wandenreich was hidden from the Soul Reaperd and keeping a low profile, they weren't apart of the group that threatened the balance almost 800 years later which lead the Soul Reapers to "wipe them out". so even if it was a full genocide by the Soul Reapers there was always going to be Quincy left in the Wandenreich.
also Yhwach has the power to share his soul which is then used to cultivate the Quincy powers in that person before he takes back the the part of his soul he shared, so as long as Yhwach exists the Quincy can be reborn