I agree with some of the recommendations above;

1) Focus on making sure your XML sitemap is accurate, and make sure your weightings (server priority weights) are set correctly from parent to child (category > sub-category > product detail).
2) Submit through Google webmaster tools
3) Submit partials in increments (again, good suggestion at 50k/time) and pay close attention to your index rate to see how fast these are picked up
4) you can brute force a lot of these crawls by submitting and re-submitting your sitemap(s) - as often as every day
5) For very important URL's that are not getting picked up a handy trick is to tweet them out from an account that has a positive share of voice (more followers than following)

You can sign into your Google admin console and ask Google to index your site and all sub-pages with 1-click. Usually takes a few minutes is all.

Indexing through a 3rd party should by penalize you as far as Google is concerned. Google is very clear about what they want for good SEO. It's all explained here: http://www.google.com/webmasters/docs/search-engine-optimization-starter-guide.pdf

Putting that many new URLs on a new domain in the system may trigger a manual review. I would probably start putting 50K at a time over the course of 1-3 months.

Also best way to get those deeper URLs indexed are:

1) Setup the XML sitemap in webmaster tools.
2) Setup easy to crawl HTML sitemaps. Web pages with ~100 links per page that are easy to crawl and navigate through pagination.

I would recommend not to use any of the mentioned techniques, instead try this

1) Upload a sitemap to Google Webmaster tools
2) Fetch as google in webmaster tools (website and some categories)
3) Create social profiles such as Twitter, Pinterest, Facebook and put your URL there. These sites have very high authority and get indexed all the time. Share the link in posts
4) Do cheap stumble upon discovery
5) Do cheap Reddit paid Discovery
6) Bookmark site in Delicious - just there
7) Write 10 blog posts, drive traffic to them through PPC, have a link back to categories or website
8) Submit RRS feed
9) Set up small PPC budget and get some clicks for very long tail and cheap keywords. Even if you get a lot of impressions and no clicks this is still visibility to google. So bid just enough to be on the first page and for the keywords that are cheap. Result - few clicks, a lot of impressions, and now Google knows about your site.
10) Monitor Webmaster tools and make sure that robots.txt is not blocking any URLs

I hope it helps

I would recommended:-
1.Make clear product hierarchy.
2.Proper product categorization.
3.Create separate sitemaps for products, categories and blog.
4.Use interlinking.
5.Use rel next and rel previous on product pages.
6.Use rel canonical on pages with session ids to control crawl budget.
7.Try to include more products on main categories instead of dividing them to multiple pages.
8.Use breadcrums.

Well, if so, there are steps to do it yourself, but the most important step according to me is URL inspection, once you do it well, delivering sitemap information to Google helps because it will be queue up for crawling and all the URLs in there should get indexed quickly if they meet Google's quality standard.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath

Getting 250,000 product pages indexed quickly and in a whitehat way requires a strategic approach. Here are the best practices to ensure that your pages are indexed efficiently without risking penalties from Google:

### 1. **Create a Comprehensive XML Sitemap**

- **Generate a Sitemap:** Ensure that your sitemap includes all 250,000 product pages. You might need to split it into multiple sitemaps if it exceeds Google's limit of 50,000 URLs per sitemap or 50MB in file size.
- **Submit to Google Search Console:** Submit your sitemap(s) to Google Search Console. This will notify Google of the existence of your pages and facilitate quicker indexing.

### 2. **Optimize Internal Linking**

- **Site Structure:** Ensure a strong internal linking structure where your product pages are easily accessible from your homepage and category pages.
- **Navigation:** Use breadcrumb navigation to enhance internal linking and make it easier for search engines to crawl your site.

### 3. **Content Quality and Uniqueness**

- **Unique Descriptions:** Ensure that each product page has unique and valuable content. Avoid duplicate content as it can hinder indexing and ranking.
- **Rich Media:** Include high-quality images, videos, and detailed product descriptions to make your pages more engaging and valuable.

### 4. **Use Google Search Console's URL Inspection Tool**

- **Manual Submission:** For key pages, use the URL Inspection tool in Google Search Console to request indexing. This can be particularly useful for priority pages that need to be indexed quickly.

### 5. **Leverage Social Media and Backlinks**

- **Social Media Sharing:** Share your product pages on social media platforms. While this alone won't ensure indexing, it can drive traffic and increase the likelihood of Googlebot crawling your site.
- **Backlink Building:** Acquire backlinks from reputable websites to your product and category pages. Quality backlinks signal to Google that your pages are valuable and worth indexing.

### 6. **Monitor Crawl Budget**

- **Server Performance:** Ensure your server can handle the increased load. Slow server response times can limit the number of pages Google crawls.
- **Robots.txt:** Make sure your robots.txt file is correctly configured and does not block important pages from being crawled.

### 7. **Utilize Structured Data**

- **Schema Markup:** Implement structured data (schema.org) to help search engines understand your product pages better. This can enhance your visibility in search results and facilitate indexing.

### 8. **Use Pagination and Canonical Tags**

- **Pagination:** For large categories, use pagination correctly and ensure rel="next" and rel="prev" tags are implemented.
- **Canonical Tags:** Use canonical tags to indicate the preferred version of a page, especially if you have similar or duplicate content.

### 9. **Regular Updates and Fresh Content**

- **Update Content:** Regularly update product descriptions, prices, and other information to keep your content fresh.
- **Blog and Guides:** Create related content such as blog posts, buying guides, and tutorials that link to your product pages.

### 10. **Performance Monitoring**

- **Google Analytics and Search Console:** Regularly monitor your site’s performance using Google Analytics and Google Search Console. Keep an eye on crawl stats, index coverage, and potential issues.

By following these steps, you can facilitate a faster and more efficient indexing process for your e-commerce marketplace in a whitehat manner. This approach will not only help in getting your pages indexed quickly but also ensure that they are optimized for better search engine performance.