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Seb-wejem
When we first started playing 5e, we skipped ahead to 3rd level. This wasn't to increase survivability, but more to allow every player to be able to set themselves up with a subclass. If I was going to increase hit points at level 1, I have a couple of ways that I would consider.
1. Add the entire constitution score to hit points at 1st level instead of the constitution bonus. From 2nd level onwards, con bonus applies as normal.
2. Give the players a bonus hit die, add constitution as normal for each hit die. This would give a fighter 24 hit points at level 1 with a constitution score of 14 or 15. Optionally, this bonus hit die would only be the set amount of hit points (or rolled hit points if you prefer that) so that the aforementioned fighter would have 20 hit points at level 1.
1. Add the entire constitution score to hit points at 1st level instead of the constitution bonus. From 2nd level onwards, con bonus applies as normal.
2. Give the players a bonus hit die, add constitution as normal for each hit die. This would give a fighter 24 hit points at level 1 with a constitution score of 14 or 15. Optionally, this bonus hit die would only be the set amount of hit points (or rolled hit points if you prefer that) so that the aforementioned fighter would have 20 hit points at level 1.