Create a universal integer sequence
Husk, 5 bytes
This prints an infinite list
ΣṖ…İ±

Try it online! or find the first index of your sequence. (Takes a lot of memory for most sequences)
Explanation:
   İ±   Infinite list [1,-1,2,-2,3,-3,4,-4,5,-5...]
  …     Rangify       [1,0,-1,0,1,2,1,0,-1,-2,...]
 Ṗ      Powerset
Σ       Concatenate

In Husk Ṗ behaves nicely for infinite lists. You can see it's behaviour here