How to connect ESPHOME device with ALEXA without HA

Probably not the direction you are looking for, however if your device is a ESP or ESP32 device you could move from espHome to Tasmota on the device and try the very good Tasmota Matter integration (briefly described at the post linked below). If your Alexa device is modern enough to support being a Matter wifi hub, then you could connect directly to Alexa using this Tasmota feature. Note if your device is a ESP 82x and not a ESP32, then you would need a 2nd esp32 tasmota device to be this bridge.