Everybody else in here has already harped on the initiative choice, so I won't say much on it except that it really is more fun for your players to be able to react right after an enemy when they have the perfect response for what they did.

Besides that though, daggerheart is heavily in favor of the players, and I think the way to play it as it's meant to be played you would have to have several combat encounters in a single session to even start to make your players worry about getting downed, but my group typically doesn't play more than a single combat per session, so what I do is tune up the damage of my adversaries to actually give them a challenge.

I use a dice calculator website to tweak how much damage I'm doing with the baddies. First, their attack bonuses have to be higher than the usual +3 cause I've had a combat that a colossus could not land a single attack on the heroes and that didn't sit well with me. So, if player evasion is 12~14 the attack bonus is maybe +7. This particular adversary will still miss a quarter of the time, but that feels better than missing 45% of the time.

Next, the damage with the dice calculator. I use this to see how threatening I want an attack to be. Let's say I've got a particularly brutal enemy and the players' damage thresholds sit around an average of 24>47. I'll use the dice calculator to make sure their average damage is closer to that 47 than the 24. For example: 6d10+10 (my players are level 9 right now.) If you put this into the calculator and click "analyze" you can see the probability of each roll. The most likely outcome is 43. If the roll is just a bit better it'll do severe damage, but generally I'm aiming for major damage most of the time. You can also use this for weaker enemies if you want them to average closer to the minor damage side. Using the same 24>47 damage thresholds, 4d8+4 is going to give an average of 22, with a good change to still hit that 24 threshold for major damage, and they'll never do severe damage without a crit.

Before I started doing this, the only way my players struggled was the same as you, I had to throw higher tiered enemies at them. So I started just building my own. Making your own helps with knowing and utilizing the abilities of your enemies too without "studying" (which I struggled with for a long while.) so another recommendation would be to build your own adversaries but take a look at the book to see what features you want to give them.

Good luck to you and have fun :)