Is it good idea to get my SSN at the same time the immigration process is starting?

Congratulations!

To prove your U.S. immigration status, you must show the INS the current U.S. immigration document, I-94, Arrival/Departure Record, issued to you when you arrive in the United States, assuming you applied for one. Obviously your spouse has put in a petition on your behalf and you would have a work permit to enter.

After the petition is approved, you will need to wait in line for your priority date (the day INS received the petition), to become "current" to apply for a green card which allows you permanent status.

you can apply for a ssn but you need to prove your legal residency, like an employment authorization, green card or a passport, you can get a ssn as a non-citizen but they'll put on it "not for work" just for other stuff you may need, so it's a better idea to get the ssn when you receive your EAD in the mail.

you wont get your ssn untill your process is finished which can take awhile but it only took 6 months for us. go to www.uscis.gov and all the info you will need is on there and they have a number for you to call and ask questions. send all the forms needed in at one time. which will be I-130, I-864, I-485, your bio info, medical exam, and its a good idea to apply to work at that time also. good luck!

did you apply for a work permit?( it's free if you apply for it with your I485 adjustment of status) I got the work permit first and I was able to apply for a SSN using just the work permit.

Did you EWI (enter without inspection) or are you an overstay (came on a visa and stayed over) or a PR ?

www.immigrate2us.net

Whatever your status you should apply ASAP to adjust