There are a few ideas that could help, depending on how you are learning Latin and (maybe) what for. (Besides a lot of experience):
- Audio: If you happen to learn from hearing (from a teacher or recordings), there is a chance that vowels are pronounced according to their quantity. Unfortunately, there's also a chance that quantities are just wrong in recordings.
- Stress: even if quantity is lost in the pronunciation (or if, like me, you are not used to distinguish them from hearing), stress falls regularly (almost always) either in the second-to-last syllable, or in the third-to-last if both of the following are short. This applies to audio and some forms of written Latin where stress is shown by an acute accent mark when it falls in the third-to-last syllable. Not sure if this counts as a stripe above letters, but at least these are not your regular quantity marks. This is common, though not universal in ecclesiastical Latin, e.g. in sǽcula sæculorum → both the u&a in the former are short, the o in the latter is long.
- Verse meters: Classical Latin poetry had quite strict rules for verses demanding short or long syllables at certain positions. (But again, you'll also find a few exceptions.)
- Some regular patterns: There are many of them that one can get used to, and predict when learning a new word. Just to give two examples: nouns ending in -tio form the genitive in -tionis (long o), plural genitive -orum, -arum endings use long o/a, etc.
Please note that a syllable can be long because of a long vowel or certain consonant configurations. Sure, this doesn't completely solve the problem, but as I said, it might help.