Giving a little fertilizer shouldn't be a bad thing. There are plenty of options available, both organic and non-organic (MG, etc.).

Personally, I use a kelp foliar spray, a kelp meal soil additive when I plant out, and at first blossoms I use Tomato's Alive! fertilizer, but in the past I used just straight MG and have had excellent results both ways.

This is my first year trying a SFG. The books says Mel's Mix doesn't need fertilizer, but my tomato plant is not growing at all. I bought an organic fish & seaweed fertilizer to use.

Espoma products are really good. You can use garden-tone or
tomato-tone for all veggies. If home-depot doesn't have it, you
can check the smaller private garden centers. I would go ahead
and add fertilizer.

Several of us on the forum have found that 1st year Mel's Mix, despite the book saying otherwise, does need fertilizer. I didn't figure it out till it was mostly too late last year. I'm on my 2nd year of SFG and veggies seem much happier with the help. FWIW, I'm using Dr. Earth, which is an organic fertilizer.