Both Google and Amazon have builtin capabilities for playing your podcast. Just publish your podcasts through TuneIn (for Amazon Alexa) and Google Podcasts (for Google Assistant). This will make your most recent episode available.
Your audience can hear your latest podcast by just saying:
"Alexa, Play [your podcast name]"
or
"Hey Google, Play [your podcast name]"
If you want to check that your podcast is available and if you don't have access to a Smart Speaker, you can use your SmartPhone instead. Just install the Amazon Alexa app and the Google Assistant app.
NOTE: Using TuneIn and Google Podcast does not use a Voice App (aka Google Action and Alexa Skill). This means that you will not receive any usage statistics and you will not own your Invocation Name. To own your Brands Invocation Name and capture usage statistics, you must have a Voice App (aka Google Action and Alexa Skill).