Hello Lala,
I can’t remember ever hearing about the DWP sending out courtesy acknowledgements, but at least you know they received it.
As to how long you will have to wait, that is anyone’s guess. Pre COVID I would have said 4-6 weeks, but now it can be any length of time. If it goes beyond 6 weeks I would suggest giving them a ring and asking when you might expect to receive a response.
Sorry not to be able to be more helpful,
Catherine
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
