Does soaking the seeds in water before you put them in seed starting mix help to speed the germination process?
Only with old seeds. See previous discussion linked below. You'll also find a FAQ about this over on the Growing from Seed forum here.
Here is a link that might be useful: Soaking seeds discussion
I tend to think that moisture plays a role in the germination of any seeds. I soak mine similar to what has been described in the link above using a napkin and a baggy. I like to use compost tea.
I germinate my tomato seeds in warm moist seed starting mix. They come up in 3-7 days if my seed starting mix is kept at about 80 degrees.
Heat alone won't do it, neither will moisture alone; but I thought everyone knew that. Life is all about balance.
I have a new way to germinate tomato seeds. It is utterly simple.
In my bathroom lavatories and showers, I keep fine wire-mesh stainless steel strainers in the drain exits, to keep hair from clogging my pipes. I put some very fresh tomato seeds... from this year's recent fruit... but fermented... in the strainers and they visibly germinate in less than 4 days. The obvious explanation is that frequent wetting by tap water stimulates germination. All I have to do is go about the business of daily life, washing, etc. Soap doesn't hurt 'em a bit, because the water flow is so much greater than any chemical presence.
I got the same results from last year's fermented-and-dried tomato seeds. (Be reminded that "fermented" means that the gel-coat has been stripped from the seed.)
I carefully migrated the tiny sprouts to a tray of composted soil... 1" thick... but with the seedlings tucked in only about 1/8". I keep this soil in a pot drainer tray, right next to the same lavatory where I wash my hands. There is only indirect, dim daylight in my bathroom, though I occasionally, briefly turn on artificial lights.
After a few days, I moved these growing seedlings outside, on the theory that they should benefit from sunlight before their "batteries" ran out. Given the various forms of abuse they suffered, from root shock to desert-like scorching sunlight, half of them perished. But half of these seedlings are roaring. So I will attempt a winter crop, here in so. Cal... in a place there the plants get several hours of sunshine, every day... beneath an eave.
I have other experimental results that upset my previous misconceptions about germinating tomato seed. My best results, prior to this bathroom strainer thing, were gained by putting seeds outside, in deep shade, in moist composted, loose soil. The seedlings prospered for many days, if not weeks, under such low light conditions. Eventually I transplanted the seedlings to tiny individual pots, and kept transplanting them as they grew larger, as they became root-bound.
It is a mistake to think that seeds, or even seedlings (which are running on battery power), need direct sunlight. What they want is moisture, moderate temperatures, and a chance to set roots in loose soil. Keep the lighting modest, in the early going; it's superfluous.
Don't desiccate your little ones with fallacious beliefs.