Paid search produces results immediately. You bid, your advertisement appears, and you can be receiving enquiries the day you start. It is also entirely rented. The moment you stop paying, the visibility ends completely, and everything spent produced customers rather than an asset. That is not a criticism, it is a description, and for a business that needs customers this quarter it is frequently the correct choice.
Optimisation is slow and cumulative. Nothing happens for weeks, and then a page that ranks continues producing without further spend, indefinitely, until something displaces it. The cost is upfront in effort rather than ongoing in spend, and the result is an asset that appreciates rather than a subscription. For a business with more time than money, this is the better trade, provided people actually search for what it sells.
The practical answer for most first year businesses is both, in sequence rather than simultaneously. Establish that the offer converts, using a small amount of paid search against the highest intent terms, because that tells you within weeks whether people who want exactly what you sell will contact you. Then invest the effort in optimisation knowing the destination works, rather than spending months earning visibility to a page that does not convert.
One asymmetry is worth knowing. Paid search gives you data immediately about which specific phrases produce enquiries, and that data is directly usable in your optimisation work. Running a modest paid campaign for a few months is frequently the cheapest research available into what your customers actually type, which is otherwise a matter of guessing.
The comparison people make wrong is cost per click against cost per click. The right comparison is cost per acquired customer, over a period long enough to include the compounding on one side and the ongoing spend on the other. Advertising that looks expensive per click can be cheaper per customer, and optimisation that looks free ignores the hours it consumed.
There is a compounding effect worth knowing about that appears when both run together. A business appearing in both the advertisement and the organic results for the same search occupies more of the page and is generally selected more often than either position alone would predict. That does not justify paying for terms you already rank first for in every case, and it is a reason to test rather than assume the advertising is redundant once the optimisation works.