Is it too late to start another batch of seeds?

[Douglas14]

I've had quite a few plants that have died after the first transplant stage...likely do to some mistakes I've made. I have a few varieties that I'd planned on, that may not make it into my garden, unless I start more seeds. I'm wondering if anyone has had success in starting seeds 4-5 weeks before planting out? If so, do these younger plants catch up to the older ones. I'm prepared to somewhat baby the younger plants, if that's what's needed. Any advice/opinions/experience is appreciated.