We don't know what he'd drunk. We only know what he SAID he'd drunk, to his mum and to the police. We also don't know how often he drinks, I had a friend who started drinking at 13 and by 16 she could drink a quarter bottle of vodka down without any discernible effect whatsoever. His 14 sister was at his "party" and left with his friends so for all we know he could be a regular drinker of several years and not drunk despite having imbibed what he says he had.
Alesha had already gotten up and been put back to bed once that night by her granddad, and she was also known to sleepwalk. The accused asked friends "how did they get her out the house though?" in his group chat conversation with friends. That indicates to me that there is something more to it - that Alesha was up when he got there and he lured her out, or that she was already out, perhaps in the garden (i doubt her feet would be clean if she'd walked to where she died, but it was a warm summer night and she could have stepped out into the garden without immediately becoming muddy). That she was out, or at least not in her bed where she was meant to be, when he came across and subsequently abducted her.