It most certainly was not her first attempt. Quite apart from the lovely collection we know as her Juvenilia, she wrote the delightfully snarky epistolary novel
Lady Susan before S&S, as well as
Northanger Abbey, a wonderfully wicked parody, then called simply
Susan. Both P&P and S&S are thought to be reworkings of earlier, epistolary novels, then called
First Impressions and
Elinor & Marianne, respectively. Sadly, those earlier drafts only survive in a few letters cited in the actual novels, so we cannot be sure if they both already existed by the time she rewrote and polished
Elinor & Marianne and had it published as
Sense & Sensibility.
But then, I do not share the feeling that it reads as a first attempt or feels like trying-out. I'm a big fan of S&S, partly because it's so down with the realities, and also because I really like Edward Ferrars. He's a man who tries to do the right thing in spite of his feelings, and he has some grey zones, but he always upholds his integrity. And Elinor wants him, and only him, so I don't see why she should need to be partnered with someone else.
As for the debate whether all that sense isn't enough for Elinor, the way I read is, the problem is that all Elinor's sense is good for the people who have to live with her, but it makes her deny herself. She needs some of Marianne's sensibility just so that she can sometimes, just now and then, put herself and her own wishes first and act selfishly and thus secure her own happiness. It's a mirror of how Marianne just now and then needs to think of others before her own feelings. It's actually quite cleverly done.
"I want you to know that you matter. I want you to know that your lives matter, that your dreams matter." (Barack Obama, 03 June 2020)