Power Up Time On Data Sheet SLUS534G - Revised 2105 Figure 18 page 16 Graph/Oscilloscope shows Timebase 400ms/Div which would result in about 2.8 Second power up.
http://www.ti.com/lit/ds/symlink/tps61032.pdf
Previous Data Sheet SLUS534E - Revised January 2012 Figure 17 page 10 Graph/Oscilloscope shows Timebase 400us/DIV which would result in about 2.8 mSec.
Adafruit PowerBoost 1000 Basic links the Previous 2012 data sheet https://learn.adafruit.com/adafruit-powerboost-1000-basic/downloads which uses TI part.
https://cdn-shop.adafruit.com/datasheets/tps61030.pdf
Placing EN pin from VBAT TO GND seems output is instantaneous, not 2.8 seconds, so I assume the Timebase should have been left at 400us/DIV not 400ms/DIV.
Could you confirm the Correct TimeBase from these two identical looking images from your data sheets?