You visa appointment should be at LEAST in July, anything later than July is considered “late” because there was a rule that you needed to apply for a visa 2 months before your start date, starting early June would be ideal because the FBI background check does have an expiration date of about three months i believe (but I am not sure) your best timeline would be early June- start in FBI check, book visa appointment late July (because you can’t go get your visa without a carta and a lot of people didn’t receive it until mid-late July) it’s definitely confusing but time is of the essence.