I want to contact a new supplier, however there is no phone number provided. The only option is to email. Should I email and wait for a reply?

Yes, if you cannot find a contact number for a new supplier anywhere, then you should still make contact however you can. Either via email or a website contact form. Make the initial contact and make your phone number obvious so that you can discuss your partnership with them if they call you. 

You can certainly sign some great suppliers even if the first contact you had was through an email.

Remember there may be other ways to find their contact number even if it is not obvious on their website. Sometimes you can find it on the Facebook page or if you google the company name and the contact number, this can find the number for you.