How quickly can your solicitor get this matter before the courts?
As your ex has blocked your number and you have no way of knowing how your dc is faring without going through the bf with convictions for violence, which would seem to be both unreasonable and fraught with potential for nastiness/fisticuffs, it occurs to me that you may have grounds to apply for an emergency ex parte residence order.
Ex parte means 'for one party'. Your ex would not be notified of your application unless or until it was granted and the first she would become aware of it would be when the order was served on her requiring her to relinquish custody of the dc to you.
However, if granted, the order would be temporary pending a full hearing of the case which is usually set within 28 days of the date of the order at which time your ex would be able to make her objections known and you would be able to set out your case for a permanent order.
My concern is for the welfare and wellbeing of a nursery-age child who may be confused and upset that she is no longer seeing her df and I strongly disapprove of any parent who plays fast and loose with contact and uses it, or withholds it, to punish or otherwise hurt the other parent.
Applying for a child arrangements order may not result in a hearing this side of Christmas, meaning that you may still be separated from your child at the time of year that is customarily all about dc.
Applying for a residence order, albeit temporary, may prove to be a way of getting this matter before the courts sooner rather than later. If a temporary order is granted and should the court ultimately decide to award custody to your ex, it should have something to say on the matter of contact that will go some way to regularise your position pending a hearing for a child arrangements order.
This course of action is unlikely to endear you to your ex, but my guess is that nothing you do is likely to please her at the present time. As I'm inclined to be proactive, I would go for it but that's easy for me to say and you need to think it through very carefully and discuss it with your solicitor who may, being appraised and made aware of the full facts, reach the conclusion that there are insufficient grounds to substantiate an ex parte application.
Whatever you decide to do, I wish you luck and hope that you are reunited with your dc in the very near future.