I have a valid F1 visa and my I-20 has a program start date of August 5th. My I-20 states that I can enter the US starting July 5th. I have my flights booked to enter the US on July 10Th. I will then leave the US to visit Panama with some friends on July 12Th and then return to the US on July 17Th. I learned that a travel signature is required on the I-20 page 2 in order to leave and re-enter the US. I have contacted the University to get the travel endorsement signature but they told me they don't provide such signature before the start of the program and that I shouldn't travel to Panama to avoid problems when reentering the US.
Since I'm a citizen of Europe, is it possible for me to apply for Esta. Ask the immigration officer to use the visa waver program instead of the F1 when entering the first time on July 10Th. Then enter with the F1 visa and i-20 when I return from Panama on July 17Th?