All of my seed packets for tomatoes, from several different sources, say to plant the seeds indoors 6-8 weeks before last frost. Now, this year that could hardly make any sense, but even in normal weather years, if I was to put my tomatoes in starter mix in February I would have skinny ass tomato seedlings by April Fool's Day. And yes, I would be a fool for following those instructions.
I would not plant my leggy tomato seedlings out in the garden at the beginning of April. I still go for a not completely conventional May 15 plant date depending on how the cool weather crops are fairing. When those are done, the tomatoes can replace them as late as May 30 (the old-time conventional date). They will grow rapidly with the soil activity up because it has warmed properly. Even when the air temps are warm, the soil may still be cool, and your tomatoes will languish. Same reason you shouldn't put your cucumbers seeds or pepper starts in before May 15. I'm not saying you shouldn't try, but if you're new to this, best stick with matching your seed starting dates to real world planting dates.
I will begin seeding my tomatoes this week. Meanwhile the broccoli rabe and fennel will need to be transplanted to the beach farm (where it is significantly cooler). The lettuce I got in a bit late, so those seeds are just popping up now. With warmer weather approaching, those tomatoes seeds should sprout and grow pretty rapidly in their little pots. I will have to keep them in check to hold off planting until May whatever.