Hello Bhavdeep Vashitha,
1. Could you please check your TMS is active and working properly by using T-Code STMS.
2. If you find any problem over there in STMS then Execute the comment r3trans.exe -din CMD. If it throw any error means, it could be a Db Connection error. Check your environment variables if necessary change and create then try again.
3. "Source system ***dc*** does not exist" --> Domain controller problem. I think so it could be a TMS problem, Please check and configure properly.
Regards,
Farkath C