I can't tell when "Morgen" tomorrow is an adverb and hence not capitalized.
Can anyone give examples of when morgen is an adverb when it is at the beginning of a sentence?
English "tomorrow" likewise serves as either an adverb (as in "The sun will come out tomorrow") or a noun ("Tomorrow is another day").
Adverbs describe how where or when an action occurs, as in "The sun will come out tomorrow". A word is an adverb if it can be replaced by an adverbial phrase like "on that day": "The sun will come out on that day." Translate the English adverb "tomorrow" with the German adverb "morgen" (lower-case)
A noun is a word that represents a person, place, thing, or idea, as in "Tomorrow is another day". A word is a noun if it can be replaced by a noun phrase like "that day.": "That day is another day". Translate the English noun "tomorrow" with the German noun "Morgen" (upper-case).
But joke aside, here are some examples for the adverb:
I think it is best to remember when to capitalize it and when in doubt just don't capitalize it (it is at least likely to be correct then):
"Guten Morgen!" (Always capitalized)
"Der Morgen ist schön" ("the morning" as a noun meaning the early hours of the day)
"Als gäbe es kein Morgen" (the nominalised form of "tomorrow", literally "the tomorrow")
morgen as an adverb at the beginning of a sentence:
- Morgen wird es regnen.
- Morgen kommt Julia zu uns.
- Morgen wird ein schöner Tag werden.
Note that all of those just use morgen by itself -- there is no article, no possessive, no determiner such as would be required before most countable nouns (such as Morgen "morning").
I'd argue the last one is a noun rather than an adverb -- otherwise the sentence lacks a subject. For the first two, you can delete the adverb and flip the verb back to its V2 location: Es wird regnen, Julia kommt zu uns.
I'd argue that it's an adverb, because: "Morgen wird es ein schöner Tag werden." --> "es" is the "hidden subject".
Also, I'd like to clarify that "Morgen" as a noun can be either "der Morgen" or "das Morgen":
"Der Morgen" = "the morning", which has no relation to the word meaning "tomorrow". If you wanted to say that there will be fine weather in the morning, it would be "Am Morgen wird es schön werden", or (tomorrow morning) "Morgen früh wird es schön werden" - or if you want to be very exact while sounding very strange: "Der morgige Morgen wird sehr schön werden." (tomorrow's morning; the morning of tomorrow).
"Das Morgen" = "the tomorrow" (see Kit845299's comment), which I think is next to never used outside "...als gäbe es kein Morgen" ("[they eat / shop / play guitar] as if there won't be another day / as if tomorrow never comes") or maybe badly translated action movies.
I've found this (literal) translation of Macbeth's "Tomorrow, and tomorrow, and tomorrow, creeps in this petty pace from day to day (to the last syllable of recorded time)": "Das Morgen und das Morgen schleicht sich so langsam hin (, zur letzten Silbe der bezeugten Zeit)."
One translation (for the stage) reads, "Morgen, und morgen, und dann wieder morgen, kriecht so mit kleinem Schritt von Tag zu Tag" (D. Tieck), another "Morgen, Morgen und wieder Morgen kriecht in seinem kurzen Schritt von einem Tag zum andern" (Schiller)... and personally, the Tieck translation feels like "tomorrow [and then another tomorrow]", the Schiller translation like "a morning [and then another morning]" - not like "one tomorrow [and then another tomorrow]".