First, ensure you have access to the Azure Storage account containing the blobs you want to transfer. You'll need the account name and access key to authenticate. You can find these in the Azure Portal under the "Access keys" section of your storage account.

Install the necessary SDKs for Azure Blob Storage and Google Firestore. You can use Python for this task, so install the Azure Storage Blob SDK and the Google Cloud Firestore SDK using pip:
```bash
pip install azure-storage-blob
pip install google-cloud-firestore
```

Use the Azure Storage Blob SDK to authenticate and establish a connection to your Azure Blob Storage account:
```python
from azure.storage.blob import BlobServiceClient

connect_str = "DefaultEndpointsProtocol=https;AccountName=your_account_name;AccountKey=your_account_key;EndpointSuffix=core.windows.net"
blob_service_client = BlobServiceClient.from_connection_string(connect_str)
```

List the blobs you want to migrate and download them locally to a temporary directory:
```python
container_client = blob_service_client.get_container_client("your_container_name")
blob_list = container_client.list_blobs()

for blob in blob_list:
blob_client = blob_service_client.get_blob_client(container="your_container_name", blob=blob.name)
with open(f"temp_directory/{blob.name}", "wb") as my_blob:
download_stream = blob_client.download_blob()
my_blob.write(download_stream.readall())
```

Set up authentication for Google Firestore. Download your service account key from the Google Cloud Console and set the `GOOGLE_APPLICATION_CREDENTIALS` environment variable:
```bash
export GOOGLE_APPLICATION_CREDENTIALS="path/to/serviceAccountKey.json"
```

Then, establish a connection to Firestore using the SDK:
```python
from google.cloud import firestore

db = firestore.Client()
```

Read the downloaded files, transform the data as necessary for Firestore, and upload it to the appropriate Firestore collections:
```python
import json

for blob in blob_list:
with open(f"temp_directory/{blob.name}", "r") as file:
data = json.load(file) # Assuming JSON format, adjust as necessary
doc_ref = db.collection("your_collection_name").document(blob.name) # Use blob name or other identifier
doc_ref.set(data)
```

Once data is successfully uploaded to Firestore, remove the locally downloaded files to free up space:
```python
import os

for blob in blob_list:
os.remove(f"temp_directory/{blob.name}")
```

This guide helps you manually move data from Azure Blob Storage to Google Firestore using Python and the respective SDKs, avoiding any third-party connectors or integrations. Adjust the code snippets as necessary for your specific data format and structure.