You can only make time
Time cannot be found nor had, it can only be made. The difference between the attitude of "I didn't have time" and "I didn't make time" is substantial: if you think of time as something you have to
I started forcing myself to think this way in late 2013, when I was sitting around one Sunday afternoon and realized that I didn't really do anything besides work. It wasn't that I spent all my time working, it was that I didn't really do anything with my time outside of work. So I sat down, made a list of the things I wanted to do, and scheduled out my week to do as many of them as I could. And in the process, I had to cut a few things that I just couldn't make time for, like rock climbing. But the liberating part of this attitude is that I no longer feel bad about not rock climbing, or say to myself "wow I really wish I had time to rock climb more," because I made a conscious choice to prioritize doing other things above rock climbing. And if I change my mind and want to rock climb instead of doing something else, I can make time for it.
Another practical example: if you feel you don't have time to do the things you want to do because you work too much, what you're actually saying is that you are choosing to spend your time at work rather than on the things you say you want to do. Staying at work until 8pm or 10pm or 2am is a choice, and by recognizing it as such you take ownership and responsibility over your time. And if your job requires you to work those hours, remember that you made a conscious choice to accept this job or career path.
Practice adopting this attitude, and I think you'll find yourself re-examining your priorities and how you allocate your time. It's much easier to tell a friend that you missed her event because you didn't have time, but it's more honest to say that you didn't make time. After all, we all get the same amount of time each day, it's up to you to determine what you make of it.
For more on this attitude and making the most of the time you have, I'd highly recommend reading the essay "How to live on 24 hours a day". Thank you to Ashna Reddy for reading drafts of this.