Can I start the process of police verification and reference letter before receiving ITA? The date mentioned in the documents will be the prior one.....Can this be a problem?
For the country you are currently resident in, IRCC requires PCC's to be issued no longer than 6 months before you submit your e-APR.
So logically, it is better to wait and get a PCC as close to the date of submitting your e-APR (by applying for your PCC after receiving an ITA).
I am assuming your nationality is Indian, so you can pretty much get your PCC done in a Passport Seva Kendra in less than a week's time - provided your current address is the same as listed on your passport and you have no prior criminal record.
If you have resided in another country for over six months and never visited it again, then you could apply for it now and submit it with your application. At their discretion, IRCC may ask you for an updated certificate later.