Things don't really work all that well without a dedicated healer. But there *are* some things you can do to work around it.

 - The first and most obvious would be to provide plentiful healing potions. Your heroes should be able to find, and purchase, these fairly easily (maybe even at a reduced price, make up a story reason if you need one). For the first few levels, healing potions make a huge difference in whether your party can stay up or is flat on it's back.

 - Make sure someone is trained in medicine and that they have a healer's kit. This can restore some vital HP as well, and they can make those checks to get flattened party memebers back up and running.

 - Have one or more fighters in the party. This is the only class that gets reliable self healing per short rest.

 - Give the average of HD when they spend them to heal. Or at least the option to take the average rather than rolling.

 - Take lots of breaks. Unlike a typical 5e party who might short rest every other or even every third encounter, this group is *likely* to need more breaks (both short and long).

 - Suggest someone take at least 1 level of cleric. This gets you access to some nice toys (including some great L1 healing spells), and if you aren't going to 20 comes with very little in the way of consequences.

Two more bits of advice on the DM side. First, start your characters at L2, if you don't have a dedicated healer, this can resolve a few of the yo-yo issues that can sometimes plague a 1st level party. The second is to reduce the damage output of your monsters. I've played around a little bit and I feel like taking the minimum of their damage rolls is too much, so maybe have each die roll be 2, or something along that line (but less than the average if you're using flat damage). 

The best advice I can give is to start at L2 and ask *one* of your players to take a level of cleric. They don't have to go full cleric, just enough that they can get a few heals off a day and keep the party standing for tough fights. This is nearly all you really need to keep a party going.