The first interstellar object, 1I/2017 ('Oumuamua) was discovered by the Pan-STARRS survey in 2017. The second interstellar object, 2I/Borisov was discovered at the MARGO observatory in Crimea in August 2019.
Although only two Solar System interlopers of definitive interstellar origin have been discovered thus far, next generation sky surveys such as the Vera Rubin Observatory/LSST (first light expected in October 2021) are expected to find more such objects. Nonetheless, the population and occurrence of these objects is relatively unconstrained.
When will the next interstellar object be discovered?
This question resolves on the date that a newly discovered interstellar object receives an "I" designation from the IAU Minor Planet Center. That is, regardless of any available "precovery" data, this question resolves when the formal "interstellar" label is given. If no objects are given this designation before 12/31/2030, this question resolves as ">12/31/30."