Blogger can index by google?

you shouldn't really be worried unless 2+ weeks has been passed since you did submit the sitemap & indexing requests,
seo is a long term game & it's slower at the start and it would take some time for the new domains for indexing/ranking,

i wouldn't advice with indexing services for new domains,
while they're not as a big problem, but many indexing services/methods use some shady methods,
spamdexing is a very good example which includes listing your website/pages in some spammy pages/websites along with many other spammy links,
you don't want that for a start, you're sending bad signals for algo that your website/pages might be some sort of spam & it's easy for new websites to get flagged

So using blogspot as an fast indexer means: write summaries of your main site content to blogspot with link back to main site, will not help get your content and internal links get indexed faster?

Your Blogspot blog will likely be indexed by Google eventually, but it can take a few days to a few weeks. Since you've already submitted your sitemap and requested indexing, give it some more time. Keep driving traffic and creating quality content to boost visibility.

If good content leads to faster indexing, Google will eventually rank your content.

Indexing and crawling rates are slower than usual across, you need to wait for few weeks. if it's urgent, then you can raise a manual indexing request on GSC

RMX said:

Indexing and crawling rates are slower than usual across, you need to wait for few weeks. if it's urgent, then you can raise a manual indexing request on GSC

Click to expand...

Same slow insexing rate,waiting weeks with use the google API?
Does google not lie to you to use their API only for indexing job posts?

But not for the big media sites right?
They post a lot of non job posts and use the google API for immedietley indexing- right?

Don't be evil- right?

Depends of the keywords and content

Then the normal way would be the best, setup fresh domain wp installation, write 10-15 articles interlink them all,, setup your eeat, author, policy whatsoever, your categories , your sitemap, then go to google console and add your property, fetch it and it should be indexed within a few days.
Then after that you can setup API .