I need people to identify this method, because I couldn't find anything similar.
I learned this from someone I can't really remember (maybe it was Milán Baticz? It was 15-20 years ago...).
It is beginner method for SQ-1, but it's a great method, low alg count yet quite efficient. I can do below 1 min average, and with an easy cube shape and no parity, I can go as low as 30 sec, and I'm not even practicing SQ-1 regularly.
Step 1: cube shape.
Standard stuff, a beginner might want to collect all edges in an 8-0 or a 7-1 configuration, and bring back the cube from there.
Step 2: solve bottom corners.
Intuitive and easy; the "hardest case" is inserting the last corner with R2 U R2 U' R2 (but in SQ-1), but that can be avoided in a lot of cases.
Step: solve 2 adjacent bottom edges.
One alg here: (1,0)/ (-1,-1)/ basically acts like an M2 move on the edges.
Step 3: orient edges.
3 cases here, but for a beginner one is enough: swap UR and DR edges:
(0,-1)/ (0,3)/ (0,3)/ (1,1)/ (-1,-4)/ (0,-3)/
I know one more alg, for the case where UL, UB, DB, DR are misoriented:
(1,0)/ (-3,0)/ (-1,-1)/ (4,1)/
The last case is: L shape bottom, I shape top misoriented edge: I just do an "M2" move, and I'll get the first case.
After this, the bottom layer is either solved, or almost solved (with 2 adjacent edges swapped); but that's okay, see Step 5.
Step 4: permute top corners.
2 cases here, one is enough for a beginner: swap UFR and UBR corners:
/ (-3,0)/ (3,0)/ (3,-3)/ (3,0)/ (-3,0)/
But the diagonal swap is also easy to learn:
/ (3,3)/ (3,0)/ (3,3)/ (3,0)/ (3,3)/
Step 5: permute edges (minus parity).
There is a short alg that swaps DL-DF, and UF-UR edges:
(1,0)/ (0,3)/ (-1,-1)/ (1,-2)/
With this we can permute the top edges in any way: for the top, we adjust U moves, while on the bottom we always permute the same two edges (that's why it didn't matter if they were already swapped after Step 3).
This alg is enough to solve the top (and the bottom) layers with some repetition of this single short algorithm; apart from parity.
But I also recommend to learn Ua and Ub edge permutation: they are fairly easy and fast, and helps greatly: almost every case can be solved with 2 algs in Step 5!
Step 6: parity and middle layer fix.
Standard stuff, not gonna detail here. I use a single parity alg. But since it's quite long, for a beginner there is a way: "break the cube form, bring it back in an other way". If you do it in the right way, the SQ-1 will be in a mixed up cube form; but parity will be guaranteed to be gone.