It's a choice to become happy. It sadly won't happen by itself and if you do nothing to become happy, you'll most likely never be.
The path to become happy isn't instant though, it's much more complex than flipping a light switch, it's definitely harder for some than others (and possibly even impossible for some sadly), but for sure, you need to decide to become happy if you ever want to be.
I think that I would say that we can't choose to be happy, but we can choose to be content, and we can choose not to dwell in sadness. We can allow our emotions to fluctuate and not stay fixed in depression. We do this by not fixing our thoughts, and by being open to the present moment.
Jordan Peterson, who for a long time I wrote off as a crackpot until I actually paid attention to some of his interviews and lectures, talks a lot about this. Happiness is a pretty crappy goal to have. It's a side effect of pursuing actual, worthwhile goals. People need to take some responsibility for their own state of mind and the things they are choosing to do that affect it.
Some of what he says is a bit disturbing, but he has a lot of statistics and cites a lot of sources that seem very credible, and I've yet to come across any counter-arguments that are anything more than incredulity and ideology. I'd love to see a plausible and knowledgeable counter argument.
Not everything he says is off base and he does present the basics of clinical psychology well. Cognitive Behavioral Therapy is an interesting field one can gain a lot from studying. However many things he talks or just hints at can be questional and neither his expertise nor fairly presented.
It helps his cause that many criticisms of him are terrible and involve many fabrications.
Well that's very entertaining, but sill doesn't engage with his actual points directly. "You have rules - have a purpose in life, and we have rules - gender pronouns". That's not an equivalence. Peterson's rules are just guidelines, in Canada the gender pronoun thing is a legally compelled requirement under which Peterson's University tried to officially discipline him, not a guideline.
Fobbing that off as "well he's just being mean to us nice people", when they went after his career and means of supporting his family (at the time), doesn't cut it.
People take responsibility for their own mind. To the point that they see basic emotions as sins in both themselves and others. To the point where unhappiness is seen as something wrong with you and something you should not talk about.
Also, worthy goals often bring pain. They often require you to forego own hapiness for something you consider more valuable. They often leave you burnout, feeling empty, unsatisfied and tired maybe even ressentfull. In particular, caregiving work is often like that. Soldiers also follow goals worthy to them (whether you personally agree or not with this or that goal) and are not happier in the result - it is called sacrifice for a reason. Those two are just obvious examples, not the only ones.
In addition to all that, your own happy personally worthy goal often brings unhappiness to somebody else, often to familly. It is extremely unfair to then blame that person for his or her own unhappiness since that has a lot to do with mine (or yours) decisions.