As someone controlling projects it's sometimes hard to get into the action with others around me, the best way is to talk to those people, to be involved to offer anything you can; perhaps not opinion, but fact to start off with. Over time working with people this way I've always found you are invited into the more intimate meetings, the nuptials of the project, if you will.
This is a natural, human, process. Great, or grand, projects such as Nasa's probes to the outer planets in the 1970's had much press attention, indeed some projects such as Nasa'a Magellen probe of the 1990's had press not only present, but directly interacting with the engineers and scientists (and then writing excellent books - "The Morning Star" by the late Henry S F Cooper anyone).
However, the mundane and private enterprise contains projects of a lot less public interest, indeed they are private interactions. And if as a member of a company you've not yet had time to foster those friendly interrelations to gain constructive access to the meetings about a project you do find yourself as the Outsider.
You can hop and jump and try to peer through the murky world of hints and conjecture, but without getting up and digging into the project this can be hard work. You may just want to help, but those inside the project might perceive you as stepping on toes, or going beyond your bounds of responsibility.
This is where the management have to see something, if you're already in a position to approach the project as a higher grade or manager role and offer yourself into the loop, that's easy and relates back to building bridges. But if you're not, management have to recognise and apply you to the project.
Beyond team membership, stepped aside from the scrum master, and not overarching the product owner; to use the right buzz words, that is you have to literally be a fly on the wall and then slide yourself into position to help, rather than hinder.
How you do this is dependent on the people, you can offer code review, document review, hints or tips on hardware or architecture. You can assist the team members or scrum master, even getting a round of coffee in can be that little bit which helps keep the folks on track.
But without yourself oiling the cogs of development with presence, approachable and an obvious willingness then you will likely remain the Outsider, you won't be on the ground floor for development meetings, you won't be in the loop with e-mail about project, you won't even know what is going on around you. If you end up in this situation, you need to address is up the chain, to push for somewhere to help yourself fit.
You always need a good manager above you to help with this, and in return you need to help them in order to help yourself.