No. it is not possible to visit Tibet without a Tibet permit. No international travellers can visit Tibet without a Tibet permit. According to Tibet travel regulations, No independent travel is allow in Tibet. All foreign nationals must get this permit before they arrive in Tibet. Only a local Tibetan travel agency can help you make this document in Lhasa.
Tibet Travel Regulation clearly states that all travellers to Tibet must have a tour organized with a local Travel agency in Tibet. Therefore this Organized tour means the arrangement of Local tour guides, Private cars and Tibet travel permits by a local travel agency. At all the entry and exit points to Tibet, they check for the permit, passport, and Visa.
It takes 2 to 4 weeks to make all these arrangements, depending on the duration of your journey in Tibet and the places of your visit to Tibet. So it is recommended for all the travellers to contact the travel agency well in advance.
Suppose you have no time to make a permit and other arrangements. You can still visit the Tibetan Inhabitat region in different provinces of China. Namely Sichuan, Qinghai, Yunan, and Gansu. These Tibetan area doesn’t require a Travel permit to visit.