Police were called to the gated grotto at around 2.35pm on Monday and a large cordon remained in place, including the cave and adjacent marshland today, reports Liverpool Echo.
Officers said the victim will be supported by specialist detectives as enquiries continue at the scene, including forensics and efforts to obtain CCTV.
Detective Inspector Paul McVeigh, from Merseyside Constabulary, said: “This investigation is in its early stages, and we are looking for any information, including anyone seen in suspicious circumstances at or near to the location yesterday afternoon.
“We understand the concern that such a serious and distressing incident will have to those who live locally or frequent the park. As with all such investigations, it is vital that thorough enquiries are completed as soon as possible to establish the circumstances, and we will be be supporting the victim and her family throughout.
“Please do not speculate or share anything which could jeopardise this work, and come forward immediately with what you know.”
Anyone with information is urged to contact @MerPolCC or Crimestoppers anonymously on 0800 555 111 with reference 23000007586.
A bicycle was today seen in the cordoned off area of the park.
The grotto is an example of a Victorian rockwork cave, which, as Liverpool Echo says, were formerly popular in public parks.
