I moved your topic to an appropriate forum category @bortek.
In the future, please take some time to pick the forum category that best suits the subject of your topic. There is an "About the _____ category" topic at the top of each category that explains its purpose.
Configure network: When the indicator light on the back flashes quickly, turn on the phone's Wi Fi connection named WIFI_ Clock or VFD_ Clock's password free Wi Fi. After connecting to this Wi Fi, the networking interface can pop up normally.
What this is describing poorly is that the clock has a mode where it produces a Wi-Fi access point. When you connect to that access point, you can then open a configuration web page served by the ESP8266 in your web browser. I'm guessing they use a captive portal to make this page open automatically, but they also specify how you can open it manually if that doesn't work:
If the webpage does not pop up, open the browser and manually enter the address 192.168.4.1 to open it.
When you open that web page, do you see a link or any identifying information? It might be that there is an open source firmware running on the ESP8266, but the seller didn't provide this information. If you can get some identifying information about the firmware, you might then be able to track down the source code on the Internet. If you found it, that would give you a great starting point for your modifications.
I noticed there seems to be a serial port. It might be possible to upload replacement firmware using this port. You would need to solder some PCB headers and get a USB-serial adapter.
If you upload new firmware, you will lose the original firmware. I don't know if it's possible to back up the existing firmware so you can restore it later if your new firmware dies not work. Worthwhile researching that.
I've built quite a few VFD clocks and one with a display similar to yours. In fact it is quite an obsession of mine. The main (but certainly not the only) difficulty you'll have with writing replacement firmware for that ready made clock is reverse engineering the schematic including display connections and working out how to use the VFD driver chip(s) on it. For the rest, there are enough ESP clock projects around as a starting point and anyway you really only need a few lines of code (if you hard code the WLAN credentials, time zone etc.). Of course it is better to also run a web server on it for such configuration settings.
Here are couple from my collection (sorry about the picture quality). The smaller one I made quite recently and documented here: ESP32-C3 Supermini clock with VFD display