If you don't have any bench to bench press on, here are some alternatives for your home gym.
I don't have the ability to bench press in my home gym. I am planning to get the right equipment that allows me to bench within the end of this year. I want to make sure I am able to bench much higher than I was able to during early 2020. Here are some alternatives that can help achieve that.
Floor press: This is an exercise that I am using. It is a partial, but it does help develop explosive power more so than the regular bench press. If I arch my back I do get a very good range of motion too. All of this should help many people increase the bench press. Simply hip thrust the bar into position (on the floor) and then safely proceed to carry out the movement.
Weighted push ups: When it comes to how the bench press feels, the weighted push up comes close to it regarding the time under tension aspect. Weighted Push ups allow you to get more out of less weights because a certain percentage of the resistance is coming from your bodyweight. I like doing the close grip push ups as it also hits your triceps a little bit more. A stronger weighted push ups will result in a stronger bench.
Overhead press: This is not really a good replacement for the bench press. However, with the previously mentioned exercises, this can assist in developing the bench press. The press is a longer range of motion. There is a lot of core and other small stabilising muscles in use for this movement, which can help the bench. Paused press (which I do not do) can help the bench even more as it hits the upper chest.
Dips: This is a great exercise. I currently do not use this as I am using the first three exercises, but this is a good substitute. Not everyone should be going too deep on this so make sure you go as low as your anthropometry allows you while being safe. You can do high reps, or weighted, or with bands. You can do dead dips which requires you to be resting with the feet on the floor while you are at the bottom, and then start from there.
This is another exercise where you can get more out of less weight.
Other variations of push ups: Bodyweight push ups, push ups with different grips, band push ups, decline push ups, clap push ups, all can help and can be added to your routine.