Is it possible to implement dependency injection without using service locator at the start of an application?

You misunderstand what a Service Locator is. You do understand the part that it is an anti-pattern, which is good, but what you're missing is that the pattern is not about the mechanics, but the role it plays in the application. In other words:

A DI container encapsulated in a Composition Root is not a Service Locator - it's an infrastructure component.

There is nothing inherently wrong with calling the class encapsulating the DI container bootstrapping code ServiceLocator, but you could also call it a Startup, Bootstrap or ContainerWrapper, it is just a naming convention.

On the other hand ServiceLocator as a design pattern is usually considered an anti-pattern since it becomes a hard dependency for the rest of the code and makes changes and testing hard and unpredictable. In your code it is Resolve<T> method which you would want to stay away from to avoid the consequences.

https://en.m.wikipedia.org/wiki/Service_locator_pattern

And to answer your question, a piece of code is usually required to initialize the DI container in any case even when it is hidden from you as part of a bigger DI framework itself, some frameworks though allow configuring your container from the configuration file too. Hope it helps!