As far as I searched, I couldn't find something valuable but is there any combinatorial (or computable) gadget for knots to guarantee them to be smoothly slice?

For example, by the virtue of the great article of **Freedman**, topologically slice knots have such gadget in the following fashion:

**Theorem**(Fre82): If $K$ has Alexander polynomial $1$, then $K$ is topologically slice.

But the converse of the theorem is not true due to the work of **Hedden-Livingston-Ruberman** in HLR12.