Begin by ensuring you have Python installed on your system, as it will be used to script the data transfer. Install necessary libraries by running `pip install requests elasticsearch` from your command line. These libraries will help you interact with the SpaceX API and Elasticsearch.

Utilize the `requests` library to access the SpaceX API. For example, to fetch the latest launch data, use:
```python
import requests

response = requests.get('https://api.spacexdata.com/v4/launches/latest')
spacex_data = response.json()
```
This step involves fetching data from the API and parsing it into a JSON format that can be easily manipulated.

Analyze the structure of the data received from the SpaceX API and transform it into a format suitable for Elasticsearch indexing. This might involve creating a dictionary that aligns with your Elasticsearch index schema. Ensure all necessary fields are correctly formatted.

Download and install Elasticsearch from its official website. Once installed, start the Elasticsearch service. Configure Elasticsearch to run locally by editing the `elasticsearch.yml` file, typically located under the `config` directory, to ensure it's accessible via `localhost`.

Before sending data to Elasticsearch, you need to create an index where the data will be stored. Use the following command to create an index through the Elasticsearch API:
```python
from elasticsearch import Elasticsearch

es = Elasticsearch()
es.indices.create(index='spacex_data', ignore=400)
```
This step sets up a new index named `spacex_data`, ready to receive documents.

Use the `elasticsearch` Python client to insert the SpaceX data into your Elasticsearch index. Here’s a basic example:
```python
es.index(index='spacex_data', id=spacex_data['id'], body=spacex_data)
```
This command sends the JSON data from the SpaceX API to the `spacex_data` index in Elasticsearch. Ensure you map fields appropriately to fit your use case.

After the data is indexed, verify the transfer by querying the Elasticsearch index. You can do this via the console or using a Python script:
```python
result = es.search(index='spacex_data', body={"query": {"match_all": {}}})
print(result)
```
This step checks that the data has been successfully stored in Elasticsearch, ensuring the transfer was completed correctly.

By following these steps, you can transfer data from the SpaceX API to an Elasticsearch index without relying on external connectors or integrations.