As mentioned on the official webpage
https://exam-practice.com/toefl-report/How long does it take for universities to receive your TOEFL scores?ETS sends your TOEFL Report only via courier. Your TOEFL report will not be sent via email. Unlike other standardized English Test, TOEFL scores are strictly sent via courier. So, it is quite obvious that it will take several weeks before the universities receive your TOEFL report.
If you choose which schools to send your scores to before you take the TOEFL, your score report will be mailed to the schools you designated 13 days after you take the exam (you’ll receive your scores 10 days after you take the test). If you choose to send score reports to schools after you’ve already received your scores, your TOEFL score report will be mailed 3-5 business days after your order is received.
After your TOEFL score reports are mailed, it will take about 7-10 days for schools in the United States to receive your scores, and longer, about 4-6 weeks, for schools outside of the United States to receive your scores.
When you estimate your time for schools to receive your score, remember it takes for your scores to be sent (up to 13 days) to reach to your university or schools. The shipping time itself (up to 10 days for US schools and up to six weeks for international schools)
For US schools, your TOEFL scores will be received about three weeks or slightly longer after you have submitted your score report, and for international schools, it can take eight weeks or longer. There is no rush or priority shipping for TOEFL reports.