Is it possible to connect my 2017 macbook air to a studio display?

No.

• The Compatibility section of Studio Display - Technical Specifications includes the line "MacBook Air (2018 or later)".
• MacBook Air (13-inch, 2017) - Technical Specifications says that your Mac has Thunderbolt 2 ports (with the Mini DisplayPort connector) and supports one external monitor with a resolution of up to 3840x2160 pixels.

I assume here that you are talking about the current Studio Display, and not about any of the 20+ year old Studio Displays that Apple sold between 1998 and 2004.