Warning: this Christianity- and Christmas-themed post may offend or disgust. The procedure described is unpleasant for the receiver.
Fertilisation of an egg cell requires sperm to reach it, which does not require breaking the hymen. A thin tube, such as a hollow straw or reed, can be inserted through the small opening in the hymen to pump sperm (obtained via male masturbation) into the vagina. The simplest way to pump the sperm is to suck it into the straw with one’s mouth and then blow it out. Another way is with an enema pump (bulb syringe) that can be constructed with primitive technology: a hollow leather ball glued to a reed using resin, tar or bone glue. The seams of the leather ball can be waterproofed with tar. The ball can be made to spring back into shape after squeezing, e.g. by constructing it with wire hoops or springs inside.
Successful fertilisation with the above method likely requires many attempts, because the probability of pregnancy from unprotected sex during the most fertile part of the menstrual cycle is 30%. Sexual activity causes hormonal changes in the female organism that facilitate fertilisation, which a simple reed insertion probably does not, but it may be possible to create similar hormonal changes with an erotic massage.
The above method can be used to arrange a virgin birth in a primitive society. No miracles are required, although a virgin giving birth may be marketed as miraculous.
Modern in vitro fertilisation technology of course expands the range of ways to engineer a virgin birth.