ESP8266 ESP-01 internal pull-up at pin GPIO0? +GPIO2 doubt
The internal pull-ups are not active at startup. The pins for io 0 and io 2 are boot configuration pins. The PCB decides the configuration, not the esp8266. The ROM bootloader of the esp8266 reads this pins and depending on the state of the pins it decides about boot process.

The io 0 must be HIGH for normal boot. With io 0 LOW the esp8266 boots into flashing mode. So you must provide external pull-up.

Read the Hardware design guidelines before designing a PCB.