Can I create an empty index from the API?

You can not create an empty index from the API.

You will need to have saved at least one record record into it at the point of creation as shown below:

https://www.algolia.com/doc/api-client/getting-started/install/javascript/?client=javascript#test-your-installation

const algoliasearch = require('algoliasearch')

// Connect and authenticate with your Algolia app
const client = algoliasearch('OA5TOH2VFB', 'YourWriteAPIKey')

// Create a new index and add a record
const index = client.initIndex('test_index')
const record = { objectID: 1, name: 'test_record' }
index.saveObject(record).wait()

// Search the index and print the results
index
.search('test_record')
.then(({ hits }) => console.log(hits[0]))

Just using the initIndex method standalone will not create an empty index. 

The initIndex method doesn’t create a new index on Algolia’s servers. It creates an index object you can interact with—for example, to add records.