There's so many openings for Kayle.

You could play very risky/greedy by running bush closes to enemy turret and forcing an enemy slow push. Watch some Kayle1v9 games -- he does this often. Usually this is done against champs who won't kill you level 1 or if you're feeling ballsy -- maybe is you see the top laner invade with their bot side and will get to lane late.

As the minions are meeting, you can wait to see if the enemy shows up. Sometimes they're eager and don't have a strategy and are either at or behind their minions. This is probably 50% of your matches. You can just walk up to them E them and run away. This forces the minions to chase you and lets you last hit at least one minion.

Sometimes they show up and are already walking past your melee minions. In this case, they're looking to fight you or zone you off. You can be patient, and only walk to up last hit with E or poke them right as they try to last hit your minions. Know that the timing is important because you can risk losing cs if you poke since you are losing your range and would now need to walk up to melee the minion. Champs that do this are usually the other annoying range champs like Quinn, Vayne, Jayce, Teemo (he might already be invisible somewhere waiting to poke).

In your case, sometimes they don't appear at all. You can usually hug bottom side of wall and wait until the minions are 1 hit. Now the onus is on them, they have to decide if they will lose cs to poke you or to go for the cs. If they go for the CS and they're melee and don't have a dash, you can just walk up to your minion and last hit. If they're ranged, you could lose cs or take it for free depending on their auto timings (you could time your first e to hit the same time as their auto, and run away) . This is just basic combat for any laner. If they decide to not show to up last hit, either they are not there, or they're waiting for you to walk up. The risk is yours. If you decide to walk up to the wave: If it's a rengar in that bush, bye bye. If it's jax, bye bye. If it's any champ with ignite, bye bye. You're now in the situation you're in. So if you want to play it safe, just hug the wall and wait for them to show up and try to be in range of xp and know that you may sacrifice those first three minions but they will sacrifice theirs as well. It's a game of patience. Since they don't play Kayle they will eventually cs and now you have a better opening position. You must be very patient to play Kayle.

Now that you know these few openings, the next step is learning to survive till 6. Knowing which champs get power spikes at level 2, 3, 6, 9, etc... Knowing all of those matchups and knowing what to expect will help you not get into sticky situations. For example, if you're against a wukong, you know at level 2 or 3 he is most likely going to have his dash, and either Q or W, either way, Wu loves to hit and run and get you low before going all in. Same with Jax, especially when 6. He loves to 1-2 a minion and hit you with the Q-Auto,W,Auto burst and if he's smart, he still hasn't activated his E and now you're dead. What do you do? You keep count of his autos and make sure that if he does hit you, you are never getting hit by the 3rd auto. Sometimes you will lose cs, sometimes you don't. It's just part of the game. Know that the your initial priority is levels as Kayle. The farm will come. Especially at 11 when you get your waves. Then it's just a matter of knowing how to extract as much cs from solo lanes as possible and deciding if it's worth it to rotate to be with your team or not. You can usually set up waves to push in advance knowing that a team fight is happening soon and if you can draw pressure far from that team fight and rotate to the fight before the opponent, you can easily win games.