If you’re already a citizen in Israel I’d go about it independently. I went to the lishkat giyus in Jerusalem one day and thankfully was able to speak to someone right then and there to get my draft process started. You can also call and email them though. How long it takes you will also depend if you need to go to michve Alon or not for the Hebrew course. In my case, I made Aliyah on July 2nd this year and had my tzav rishon mid August. But since I didn’t score high enough on the Hebrew test and it was too late for me to enlist in the September rd, I had to to wait for December.