Latvian's first week can move faster than many languages, precisely because the alphabet and pronunciation are so learnable early — the trick is not rushing into the case system before you're ready.
Learn all 33 letters, including macrons (ā, ē, ī, ū) and carons (č, š, ž) — see Latvian Alphabet. Because spelling is close to phonetic, this stage is genuinely achievable in a couple of days of focused practice, faster than in most languages.
Practice noticing that stress falls on the first syllable in the large majority of words, and start listening for the length difference between short and long vowels — these two pronunciation features shape how the whole language sounds.
Learn common nouns in their dictionary (nominative) form together with their gender — don't worry about case endings yet. A small vocabulary of everyday words, correctly pronounced, is a solid week-one goal.
See also the reference page: Latvian for Beginners.
Often within a couple of days of focused practice, since Latvian spelling is close to phonetic — faster than the equivalent stage in many other languages.
No — build vocabulary in its base (nominative) form with gender first; case endings are much easier to add once you already have real words to apply them to.
First-syllable stress and the length distinction between short and long vowels — both shape how the entire language sounds and are worth prioritizing from day one.
Not to the language's actual learnability — it mainly means fewer readily available resources, not that the language itself is harder to learn well.