As a Galio main, I should admit that it is really hard to cs with him till you get some mana since his AA animation is really slow and he is melee (i'm playing him mostly mid lane (he is a bit stronger midlane since he got really nice damage with Q, E and ult but absolutely no constant damage) so it is kinda a disadvantage). He kinda has the worst AA of the game as an melee ap champion that has no interaction with his AA
So before my first back, what I do is I try to see if the creep i want to last hit is being AA by my minions. If he is, I click on him just before the allied creep's aa is hiting him because with the delay of the animation, i'll actually damage that creep after the allied creep's aa hit him. Taking savagery in the cunning masteries can really help (but I don't since I usually go 18/0/12 with dft, this keysotne being way more reliable than thunderlords on Galio (there is just no good mastery on Galio)
Also if you are playing against a ranged champ, try to pay attention if he's going to harass you if you try to last hit and if he isn't going to then you can kill those casters minions for free
After you got some mana, just kill the minion's backline with spells (Q and E till lvl 9 and then Q is enough even if you don't really build ap) and try to last hit the frontline.
I usually manage to last hit the 6 creeps at this stage of the game while i'm more around 4/5 before I get the mana, so what I usually do is I first back at 650 gold and buy just a mana crystal and boots, and i take tp even midlane (but with some matchups, ignite (against veigar cuz this lane is free af so let's not wait lvl 6 to snowball), purge (ahri/lissandra/tf), barrier (lux/xerath/ziggs), and exhaust (yasuo/lb/kata) are way better (yeah i really play him mid but he's stronger there believe me)) so I can back more without having to deal with being behind in xp/creep
Also from what I've seen with your itemization you want to deal a lot of damage so I would advise you to take abyssal, you don't even need to have any ap against you cuz well 90 AP + 10% cd and 10% more magic damage does really hurt
If you wanna know this advice come from a bronze 3 (;-;) Galio main with 58.3% winrate on him and a kda of 7.9/4.1/11.3 with 181 creeps on average so I might not be the best Galio ever but I ain't bad at all with him (and 3 of my losses come from being afk cuz i have a fucking bad pc that turn off everytime he's hotter than idk like 60 degrees celsius (and 2 times i was winning lane hard (was against veigar) so let's say it would have been 2 wins one loss so it would have been 23w/13l ; 63.9 winrate but I can't be sure about that))
And I'm bronze 3 cuz well 28% winrate kassadin, 25% Zyra and 23% winrate shen, should have only played Galio (i play him support too) lmao