The phrase "after they first started" is correct and usable in written English.
It can be used to indicate a point in time following the initial beginning of an action or event.
Example: "After they first started the project, they encountered several unexpected challenges."
Alternatives: "after they initially began" or "following their initial start".
And that's almost six years after they first started making headlines.
Its stock prices did not hit bottom until 2003, more than a decade after they first started falling.
However, the girls did not release their first single "Wannabe" until 1996, two years after they first started working together.
Twenty years after they first started broadcasting together when Mayo was still on BBC Radio 1, the pair have notched up 50m downloads for their Radio 5 Live film review show.
"Next month, we will bring together world leaders in London to talk about how we can help Syrian refugees, five years after they first started fleeing brutality and conflict in Syria," Cameron said.
I don't know, but I do know that, however many years after they first started writing, I can still count on a playwright like David Hare or Caryl Churchill to give a shit.
Mature fruit bodies grow very close to the initial site of inoculation within 3 mm and take about 60 days to mature after they first start to form.
He claims he "didn't think much of it" when they first started, but after one particular headache caused him to become disoriented and start vomiting in September, it became clear that this was not a garden-variety migraine.
They gave a peek behind the curtains in February of this year — two years after they first got started — and have continued to iterate on the product since then.
Soon after they first met and started acting silly together at a local rink in Basel, Switzerland, in 1936, Frick & Frack became famous, captivating crowds with 8- to 10-minute routines.
