Please google the definition of "computer". I used this specific term and not a PC/Mac/Laptop/whatever.
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Is it possible to get a book from a library without a library?
Is it possible to access an Internet without a computer?
Is it possible to talk to another person if you the only person on Earth?
And I want to get 1 billion USD without moving my lazy butt. You may wishfully think whatever you want, you will never get it.
A server is just that, a piece of (hardware or) software which serves content to the network. If you do not have a server, there is nothing which makes the app available, hence no webapp. So, you need server!
If you just want to make your webapp available, depending on the backend language, you have different options. There are a lot of hosters out there, which let you upload PHP and NodeJS applications. Also, a lot of cloud providers let you run a dedicated application, no need for OS management. However, you might need to get a virtual or even dedicated computer, which you have to configure yourself, if you cannot host your webapp backend any other way (for example if you are using a binary server application).
Question is really vague like others said. I'll just guess you're talking about "serverless" apps which are not completely without server :) Because as soon as something is online (and I guess you don't want to distribute it by post) it is on some server.
However, term "server" is wide. It can be a peace of rented hardware with OS (virtual or not, shared hosting or dedicated) or it can be a "service" like Amazon S3, Contentful, etc.
Of course, without a database and connection to other online services (like email, facebook, etc) it will not do much (offline or online). So you can expand it with services like AWS Lambda + AWS API Gateway + AWS DynamoDB to build complex apps with dtabase and API backends, etc. It would be still considered "serverless" because you would base it on "services" and not "servers" but in practice, behind every service at the end there is a server :)