Can a couple have a Jewish wedding without a previous marriage get?
A married woman MUST have a valid get rom her first husband in order to remarry, and until she gets a get she is considered married to her first husband according to Jewish law in every way. A married woman that marries another man is a VERY serious transgression and may very possibly cause the children from the second marriage to be “mamzerim” – illegitimate, and they will have a very hard time getting married afterwards.
I would advise you to speak to a competent orthodox Rabbi, who may be able to assist you on this important matter.
If you need any help finding one please let me know.