I think how you choose to respond to her blocking you now will make a difference to how things will be in the future. Think carefully. Do you want her to see you as respectful, supportive , non threatening? Then don’t threaten her with court, or pressure her or be intrusive. Respect her personal space.
Pave the way to a good co parenting relationship.
She, not you, is the one who is pregnant. Her health and wellbeing is her priority. Having a healthy, low stress pregnancy is what she needs and deserves.
Pregnancy and birth is not without risks. Pregnancy and birth does take its toll on the body. (I knew someone who ended up in intensive care as she nearly died during childbirth from haemorrhaging blood).
She has every right to protect herself and to focus on her needs. She hardly knows you. So, tone it down a bit, back off a bit, relax, be patient and chill. Be patient and get to know each other (when she’s ready to see you again).
This is not the time for pushing for how you want things to be.
I’m sure she would appreciate it if you respect her personal space and her choice to continue the pregnancy and birth without you.
Pave the way to a good co parenting relationship.