Very similar scenario here OP.
I was also originally offering contact but Dad wasn't being consistent, going long periods without seeing our DC or just when it suited him.
When I asked for more consistency he did the "Fine I will take you to court for 50/50 and you'll get no money" thing. Typical.
My approach was to be totally non emotional about it.
"Thank you for letting me know, I will await contact from your solicitor".
I did the grey rock method on any other contact where he has tried to provoke a reaction.
As it stands it's been 6 months and I've had nothing from a solicitor... ex also hasn't bothered to see DC in this time.
I'm still prepared to receive something, but it is what it is, if he was that bothered he would have done it ASAP as I would have, money no issue btw.
I spoke to a family solicitor as well so I'll tell you what they said as my ex also lives an hour away.
50/50 could be possible, but as his contact is inconsistent it would have to be progressed to that.
The fact that he is over an hour away would also make 50/50 less likely (he moved in my case) because it's not practical when DC is in nursery. Even though nursery I suppose it's technically "optional" the court will look to the near future which is school.
If ex were to ask to have DC every weekend and school holidays say to try and get 50% or close to over the year without the schooling issue, it wouldn't be fair on me due to no quality time with our child as I would have them all in working days. So an unlikely outcome.
The only scenario where it would be likely my ex would have 50/50 I was told was if he moved close enough to make school and nursery runs reasonable.
Of course a solicitor can't say exactly what a court will do, but this was their take on the possible scenarios.