The only way to “level up” IVs is to use Bottle Caps. Since the introduction of Bottle Caps in Generation 7, they’ve become more accessible in game ( in SV you can purchase one for 20,000 Pokedollars ).
They max out one stat’s IV value, however, a Gold Bottle Cap can max out all of a Pokemon’s IVs at once. Gold Bottle Caps cannot be purchased directly, however, you can obtain them through the Porto Marinada Auction & the Academy Ace Tournament in the base game, and by registering 210 Pokemon in the Blueberry Pokedex, the Terrarium, and the Item Printer in Indigo Disk.
The process of using Bottle Caps to increase IVs is called Hyper Training, which can be done in Violet by speaking with the man with the Abomasnow near the Montenevera Pokemon Center.