There are no rules for mixing races, but...
There are no simple rules for mixing races, where the properties mix like they maybe would in the real world. That said, you have quite some options to realize your idea.
Cosmetic modifications pose no problem
You can always modify cosmetic properties of race and other character options without risking balance problems. This means that you can chose one of the races that are similar to your combination (elf, dwarf, human, half-elf) for the racial bonuses while completely making up your looks and so on. E.g. you say that you use human stats, but look like a dwarf with pointy ears. You can easily combine cosmetic modifications with the other suggestions detailed below.
Rules from TCoE allow for a lot of flexibility in features
Extensive customization options were only published in Tasha's Cauldron of Everything. The optional rules for Customizing Your Origin (TCoE p. 7-8) let you replace proficiencies and ability score increases for any race. Using these options lets you mix racial traits somewhat, by using one of the races that are similar to your combination and swapping some things to options that fit the rest. While this is not a method for mixing races, it allows flexibility which lets you assemble your vision of a mixed race.
There are some races that give many options
The Custom Lineage race option from TCoE explicitly calls out that you can make up whatever outfit you like, but you can do this with other races without balance issues as detailed above. In addition to the Custom Lineage, the variant human and half-elf race all give options to chose ability scores, skill proficiencies or even feats. These give you many options to customize things even without the Customizing Your Origin option. And while variant human and custom lineage are optional, half-elf at least is not.