There are several specific indications that the sea is at high tide. The opening words of the poem state:
The sea is calm tonight.
The tide is full...
The next indication of the high tide is contained in these lines:
Listen! you hear the grating roar
Of pebbles which the waves draw back, and fling,
At their return, up the high strand,
The tide would have to be high in order for the waves to fling the pebbles all the way up to the highest point on the strand. A strand is a strip of land that is underwater part of the time and exposed part of the time, depending on the tides.
Finally the speaker brings in the Sea of Faith:
The Sea of Faith
Was once, too, at the full, and round earth’s shore
Lay like the folds of a bright girdle furled.
The simple word "too" proves that there is a high tide at present. The speaker is saying that the Sea of Faith was once at high tide just like the high tide he is observing now.
Many people in Matthew Arnold's day were troubled by the decline of religious faith as it was being undermined by the progress of science and technology. In a few more years Charles Darwin would be publishing his book On the Origin of Species, which seemed to prove that the biblical account of creation in Genesis was nothing but a myth. Arnold's poem is important because it is a clear expression of a general malaise of the time. The fact that he can only hear the metaphorical Sea of Faith's "melancholy, long, withdrawing roar" suggests that the actual tide on the strand down below his window has reached its highest point and will begin withdrawing too.