If you are an entrepreneur or brand new company who is just starting out on creating an online presence, I bet building a website is one of trillion tasks on your plate. Many would say that creating a website is non-negotiable and is the first step to being online. Contrary to what others might tell you, it is possible not to have a website and still build an online presence, albeit a limited one.
So the answer is no, but I'd recommend this only for the short term.
The benefits of having a website far outweigh not having one, but if you simply just want to start promoting yourself online, I'd say you can start simply by just creating the relevant social media accounts (by relevant I mean the social media platform where your target audience resides).
As long as you have a URL you can share with others and the page contains your business name and contact information, I'd say that is the bare minimum for any prospect, buyer or client to know you exist and contact you.
For example, you could buy a domain name and redirect people to your Facebook business page. There, you can be in touch with your audience through messenger, gain reviews and so on.
Understand how you want to attract people will determine if you should hunker down and build a website right now.
Depending on your business and goals, it could very well be faster to build a reputation through social media or online communities to gain prospects than to take 3-4 months [citation] developing a solid website and hoping that search engines will direct people to your website.
Tonnes of companies develop and design websites that do absolutely nothing for them in terms of generating revenue, and for no reason other than to say they exist. Many social media influencers only use their website to sell their branded merchandise only after they have built a following. This proves that a website is not always the first thing you should prioritize.
If you are an artist or creative person who is trying to get showcase your work online and get clients, joining communities where it showcases your portfolio such as Behance could really be sufficient for now. Same goes for freelancers who are trying to get work, listing themselves on Upwork could be enough.
It all depends where your audience is, and how they can find you.
Just because you have a website right now does not mean you will be found, nor does it mean you have a business. If you're serious about making money through your website, direct or indirectly, then you need to start a website sooner rather than later.