This girl and I really like each other but she never initiates anything, what should I do?

Ask. There are many possibilities. Maybe she is shy, or had a bad experience, or is upset about something... The worst thing to do is to get upset about it without asking her. That will mean that when you do end up asking you will be upset and the conversation will not go as well as it might.
Why don't u . Most of the relationships people wait for the other person to do and wish they would do and waste the whole life doing that life does not wait for people like that why don't u be the one who iniate and if it it does not work out it does not u won't have regrets.
Talk. Tell her how you feel, & focus on yourself and your feelings or she may become defensive or just shut down. You may feel rejected or unwanted because she isn't initiating physical contact. Physical contact is important to any intimate relationship. Ask her if everything is ok. Maybe she is depressed or has low self esteem. Keep an open line of communication during good and bad times.