Not without an EVEMS, no.
This panel is the obsolete and dangerous old "Split-bus / Rule of Six" panel. The top 6 breakers are the main breaker, all six of them! They all must be turned off to de-energize the panel. All six should be marked "Main breakers". The bottom left, currently marked "Main" should be marked "Lighting main". It powers the "Lighting Area", or all the breakers in the section below it intended for small loads.
The original purpose of split-bus / Rule of Six is that breakers larger than 60A used to be prohibitively expensive. In their rush to electrify large appliances, the compromise was this Rule of Six design, where the sum of breakers can significantly exceed the service size. The promise was that there would always be a NEC Article 220 Load Calculation on the loads in the panel, and that Load Calculation would assure that overload is unlikely.
Of course the problem is people coming along and adding things without re-running the Load Calculation, and these additional loads overloading the panel.
So the right answer is to do a NEC Article 220 Load Calculation, such as this worksheet from Sacramento which accurately reflects NEC 220.82.
It would really help to adjust expectations, though. Here, Technology Connections has extremely good advice: you don't need anything near 60A to charge at home; that's only needed for travel.
So if you can downsize your charging circuit to something to live with, grats! You're running your EV circuit with cheap 12/2 or 10/2 Romex instead of costly #6 MC.
If you refuse to do this, then we must resort to the thing mentioned at the top - EVEMS. Since you want a 60A breaker it sounds like you're already on board with a hard-wired charge station; so now we just need to add the current sensor module and you're all set. Examples are the Wallbox Pulsar Plus with power meter (a hardwired cable data connection) , or the Emporia Load Management bundle (WiFi to the cloud for a data connection: no cloud, no charge!), or Tesla's fairly obscure offering using a Criteo power monitor (hardwired). Canadians have an Elmac unit, and Europeans have the impressive Myenergi Zappi (proprietary wireless; no WiFi needed).