Anon2, I'm sorry you had that experience - both the feeling unsupported in the first place and also the difficulties raising your concerns.
NLS should happen as part of paeds induction. For a variety of reasons, it often doesn't happen right at the start, but you should book yourself on to one if it doesn't happen. Some Trusts try to organise an in-house one for their trainees, others expect trainees to organise it themselves - but it should happen. The same as ALS, there is a list on the resus council website. Claim it back through study budget etc. There should also be departmental induction that includes neonatal resuscitation and the specifics of local policies / equipment such as how to use the resuscitaire.
What should happen, is that paeds SHOs who have not done any neonates before (this includes GP trainees as well as FY2s), should be accompanied to all deliveries until they feel comfortable going alone (EVEN if you have done NLS as part of induction). Which as a general rule, should be at least a couple of weeks, more like a month - depending on volume of neonatal calls and how quickly you get some good experience. This could be either a reg or a senior SHO accompanying. Sometimes this is challenging, especially out of hours. The most, most, important thing you need to remember, is call for help early. Many times, by the time people come running in, you will have a crying baby - but we would all much rather come and find that the baby is now doing ok, than to not be called until a few minutes later when things are not going well.
I would really advise you to put in incident forms each time you have to go alone and you felt unsupported / underqualified, even if the baby came out crying and you didn't have to do anything. It's another objective record of your concerns, and the Trust are obliged to respond to them.
As a general piece of advice for anyone who has their first paeds job coming up - it is worth checking in advance with the department, what the NLS arrangements are - whether they will organise an in-house one for you or not. Because if you have to book it yourself, they are often booked up several weeks in advance, and it is really useful to be able to do this as early into your job as possible. It can be very frustrating on day 1 to be told that you have to organise this and to then find that the next available course <200 miles away is in 6 weeks' time.