There are essentially two cases in which a superlative adjective or adverb can occur without 'the'.
One is, as you have mentioned, when 'most' is simply functioning as a rather formal synonym of 'very'.
The other is when the implicit comparison is not between one individual and others, but rather between what might be termed different 'manifestations' of the same individual, e.g.
Tom sings best first thing in the morning.
does not compare Tom's singing with that of others, but simply Tom's singing in the morning with his own singing at other times of day.
Very often, this second case is marked by the use of a prepositional expression such as 'at (my) best'.
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