Not really, I could be wrong and I'm basing my answer of an hdfc employee.
So, according to the employee, if you hold a co branded card ( tata neu / swiggy etc) and don't have a core card, then you cannot apply for a LTF core card.
That's the only catch, if you don't mind paying the joining and annual fee, you can still apply via C2C through branch for a core card.