I am not sure if this belongs here, but I am earning miles on my BAEC account with this trip, so I thought I could place it here (if not: please forgive me!)

I recently booked a trip to the Middle East with Malév (great fares, BRU-BUD-TLV, AMM-BUD-AMS for €250ai!)

On my way back, however, I have a very tight connection in Budapest. My flight from Amman arrives at 06:30 and my connecting flight to Amsterdam leaves at 07:05. This gives me 35 minutes between flights. I was quite hesitant to book this, but I spoke to a Malév representative and she ensured me this was an "official connection", so I should practically be able to make it. I decided to book it.

But now I am actually wondering if I will be able to make it (we are a 8-person group, which will probably slow down the process of getting from gate to gate). Will I have to clear immigration (for entering a Schengen country) and customs first? Or will I go straight to the next plane? Flights both arrive/depart from terminal 2B, so no terminal change!!

Would there be any chance that I could make this connection? Any tips on connecting in BUD would be greatly appreciated!