No, Redis doesn’t have a notion of a global/default TTL and yes, you do have to set it for each key independently. However, depending on your requirements and on what you’re trying to do, there may be other ways to achieve your goal. Put differently, why do you need it?
For example, if you want to use Redis as a cache and not worry about having to remove “old” items, you can get simply by setting the maxmemory_policy to allkey-lru. This will evict the least recently used keys whenever Redis’ memory is exhausted.
EDIT: for more information, see the helpful links in the comments below from @arganzheng and @Kristján, as well as the inline documentation in the redis.conf configuration file.