The defender is hoping to become a first-team regular in future after experiencing Europa League competition this pre-season.
The 19-year-old defender has featured on several occasions for the Hammers so far this pre-season, making his debut against FC Lusitans in the Europa League and starting against Werder Bremen last Sunday.
The youngster is one of several that manager Bilic has used in the qualifying rounds in Europe so far, and is expected to be in the squad for the tie against AFC Astra Giurgiu as well.
And Page is obviously desperate to prove himself to the new boss when given the opportunity, saying he is targeting a leading senior role further down the line.
“Every time I step out onto the pitch it feels like a dream and hearing the crowd,” he told whufc.com.
“I want to push on and become a first-team player. There are players like Mark Noble and James Tomkins who are always there to help me through it. The manager has shown trust in me to play in the Europa League and I hope there is more to come.”
Europa League a chance to catch Bilic's eye
The Hammers have had a mixed experience in the Europa League so far, with a comfortable win in the first round followed by a narrow win on penalties the next time out.
They then failed to hold on to a two-goal lead in the first leg against Astra last week, with a James Tomkins red card, their third in the competition so far, turning the tie on its head.
Page, though, is confident they can progress and says the European experience has been a good chance for the youngsters to catch the new manager’s eye.
“With the mixture of senior and young players I'm sure we can go and get the job done,” he added.
“I have never been to Romania but I'm sure it will be a good experience. This is about showing our potential and catching the manager's eye for a first-team place.”