Can you give a direct link to that product? Putting “logic gate electronics level shifter” into google gives nothing but generic references about those terms. Not that manufacterer or seller.
Also, what do you mean with lift/land 5 volt? Is that a signal or the 5 volt supply to the level shifter.
How do you determine that a program is not running? In other words that the ESP8266 is stuck/hanging/in a repetative boot? Do you have a means of detecting the SPI signals?
And what is the SPI clock rate that you are trying to send data with? Does lower clock speeds work?
As always a schematic of how you have wired this up is required to rule out mistakes.