Can I do enough Cheese damage?

Probably. if u raise Martha's 3rd skill to lv 10, then make it much more possible.

Make sure at that round, you have enough star for Jalter to trigger critical damage. If everything ready, my damage calculator tell me that Jalter will do >300000 damage for the 3rd crtical Buster card in a NP-x-B-e, even without consideration what CE used for Jalter and not using Anniversary Blonde.

Also you probably still have time to Jalter's lv6 in this 6 days, if you tried hard. Good luck on that

Short answer, probably not. At least not on the first turn.

Long answer:
To reliably(!) oneshot a pillar even the specialized servants (some zerks and xuanzang) need at least bond 7 from what i have seen. With offensive skills at 9+, specific (leveled) CEs and backup from 1-2 Wavers and Merlins that is. Sometimes you even need the Waver NP to decrease defense. I guess the requirements are not that high if it's okay to sometimes whiff on the oneshot. However, for (Bond 5) JAlter without any class advantages it probably is still too much.

Another problem is how would you manage NP charge? Merlin can only charge 20% at most. As far as I know, the only CE that would enable a turn 1 NP with that setup is Kaleidoscope. However, that lessens the overall damage potential even more.